Prudent Valuation

Prudent Valuation

Here we go

Global Derivatives Trading & Risk Management

Budapest, 10 May 2016

Marco Bianchetti

Head of Fair Value Policy, Financial and Market Risk Management, Intesa Sanpaolo

Adjunct Professor, University of Bologna

In collaboration with

Umberto Cherubini – Professor of Mathematical Finance, Bologna University

AIFIRM – Association of Italian Financial Risk Managers

M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest, 10 May 2016 p. 2

Summary [1]

1. Introductiono Overviewo Prudent valuation history

2. Theoretical Backgroundo Price opacity & financial crisiso Pricing beyond Black-Scholeso Market incompleteness & illiquidity

3. Regulationo Overviewo The Capital Requirement Regulation 575/2013o The EBA Regulatory Technical Standardso AVAs vs XVAso Prudent valuation reportingo Prudent valuation data NEW

NEW


Summary [2]

4. AVA calculationo Definitions and basic assumptionso Market price uncertainty AVAo Close-out costs AVAo Model risk AVAo Unearned credit spreads AVAo Investing and funding costs AVAo Concentrated positions AVAo Future administrative costs AVAo Early termination AVAo Operational risk AVA

5. Prudent valuation frameworko Implementationo Methodological frameworko Operational frameworko IT frameworko Documentation & reportingo Example of prudent valuation framework

6. Conclusions7. References8. Glossary

NEW


1: IntroductionOverview

Traditionally, quantitative finance practitioners are divided into two populations: thosewho seek fair values, i.e. means of price distributions, and those who seek riskmeasures, i.e. quantiles of price distributions. Fair value people and risk people typicallylive in separate lands, and worship different gods: the profit and loss balance sheet, andregulatory capital, respectively.

Prudent Valuation is a rather unexplored midland which has recently emergedsomewhere in between the well known mainlands of Pricing and Risk Management. Infact, the Capital Requirements Regulation (CRR), requires financial institutions to applyprudent valuation to all fair value positions. The difference between the prudent valueand the fair value, called Additional Valuation Adjustment (AVA), is directly deductedfrom the Core Equity Tier 1 (CET1) capital. The Regulatory Technical Standards (RTS)for prudent valuation proposed by the EBA have been adopted by the EU (reg.2016/101) on 28th Jan. 2016.

The 90% confidence level required by regulators for prudent valuation links quantiles ofprice distributions (exit prices) to capital, thus bridging the gap between the Pricing andRisk Management mainlands, and forcing the crossbreeding of the fair value and riskpopulations above.

In this seminar, we will explore the Prudent Valuation land.


1: IntroductionOverview

Q-LandQ-measure

Pricing: extrapolate the

presentFair value

Profit and loss

P-LandP-measure

Risk: model the future

Risk measuresCapital

Prudent LandPrudent measurePrice distribution

90% exit priceCapital


See A. Meucci, “P versus Q: Differences and Commonalities between the Two Areas of Quantitative Finance”, GARP Risk Professional, pp. 47-50, February 2011, http://ssrn.com/abstract=1717163

1: IntroductionP vs Q and beyond


The idea of prudent valuation dates back to Basel 2 regulation (see BCBS, “International Convergence of Capital Measurement and Capital Standards – A revised framework”, June 2004).

In particular, sec. VI (“Trading book issues”), ch. B (“Prudent valuation guidance”), par. 690-701 set the requirements for prudent valuation in terms ofo systems and controls,o valuation methodologies,o valuation adjustments or reserves, impacting regulatory capital (not P&L).

The CRR inherited most of the contents in its art. 105.

In more recent times, prudent valuation has been required by the Financial Stability Agency (FSA) to UK institutions, see refs. below.

o Financial Services Authority, “Dear CEO Letter: Valuation and Product Control”, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf

o Financial Services Authority, “Product Control Findings and Prudent Valuation Presentation”, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf

o Financial Services Authority, “Regulatory Prudent Valuation Return”, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml

1: Introduction Prudent valuation history [1/3]



August 2008

FSA “Dear

CEO letter”

November 2010

FSA “Product Control

Findings and Prudent

Valuation Presentation”

April 2012

FSA “Regulatory Prudent

Valuation Return”, Policy

Statement

2008 2009 2010 2011 20122006 20072004 2005

June 2004

BCBS “International Convergence

of Capital Measurement and

Capital Standards” (Basel 2)



13 November 2012

EBA Discussion

Paper

(EBA/DP/2012/03)

10 July 2013

EBA Consultation

Paper

(EBA/CP/2013/28)

1 Jan. 2014

CRR

575/2013

31 March 2014

EBA Final Draft RTS

and first application of

prudent valuation

28 Jan. 2016

EBA RTS

published on

OJEU

8 November 2013

EBA Quantitative

Impact Study

2012 2013 2014 2015

23 Jan. 2015

EBA Final Draft

RTS amended

Prudent valuation in

place

2016

28 October 2015

EU commission

adoption of EBA RTS

NEW


Elaborated by AIFIRM Market Risk Committee, working group on prudent valuation, 148 pages, publicy available at http://www.aifirm.it/position-

paper-prudent-valuation

Summary Executive summary Introduction Regulatory requirements Prudent Valuation scope General assumptions and considerations Theoretical background AVA calculation under the simplified

approach AVA calculation under the core approach Prudent valuation operating framework Prudent valuation technology Conclusions Appendixes References Glossary and notation

1: Introduction Prudent valuation guidelines and sound practices

NEW


Summary

2. Theoretical backgroundo Price opacity & financial crisiso Pricing beyond Black-Scholeso Market incompleteness & illiquidity


o Price opacity & financial crisisthe crisis, and the Enron case before, has introduced the problem of valuation as a mean of diffusion of losses among financial institutions and assets.

o Pricing beyond Black-Scholesthe problem of getting the price wrong is linked to the fact that, already after the 19th October1987 market crash, the standard Black-Scholes assumptions of normal distribution of assets returns and perfect replication in continuous time of all financial products proved wrong.

o Market incompleteness & illiquidityother sources of risk, not traded in the market, such as volatility and correlation (smile and skew) have surfaced as key valutation elements. The hedging problem has become more complex and perfect hedging impossible (the market incompleteness problem). Moreover, if hedging can be done (volatility swaps or correlation swaps), it has to be done in highly illiquid markets, or even with OTC transactions.

o Credit risk: “unearned credit spreads”, that is expected loss due to default of the counterparty has become the major element in the evaluation of a financial product. This has added even more focus on hedging complexities.

2: Theoretical backgroundIntroduction


2: Theoretical backgroundA history of financial crises

September-October, 1998LTCM, the major issue of the crisis is the impossibility to replicate financial derivatives in continuous time, and in perfectly liquid markets. It is the first case of incomplete markets.

December, 2001Enron, the issue is lack of transparency in accounting data. The impact was uncertainty of valuation of similar companies or companies with the same auditor (Arthur Andersen). It was called “financial contagion by incomplete information”.

May 2005Sudden drop in credit correlation triggered losses in financial intermediaries absorbing equity risk in securitization deals. It was a case about correlation uncertainty and hedging risk. Equity hedging strategies based on mezzanine were turned into losses by a major decrease in correlation.

2007-2008 Subprime crisis. The crisis themes were illiquidity, lack of transparency and an increase in correlation (systemic risk). On top of that, the peculiar issue of the crisis was the role played by the accounting standards in spreading contagion across intermediaries.


2: Theoretical backgroundAccounting and the subprime crisis

What is the link between financial crisis and valuation?

“Default losses on US subprime mortgages about 500 billion dollars.

But in a mark-to-market world, deadly losses are valuation losseso Valuation losses as high as 4 trillions. o Major banks failed without a single penny of default

BIS study of rescue package: 5 trillions in committed resources. “

Eli Remolona, IV Annual Risk Management Conference, Singapore, July 2010


2: Theoretical backgroundToxic assets

. “Financial assets the value of which has fallen significantly and may fall

further, especially as the market for them has frozen. This may be due tohidden risks within the assets becoming visible or due to changes in extremalmarket environment”

FT Lexicon

Toxic assets are a matter of:o Liquidity (“market frozen”)o Opacity and ambiguity (“hidden risks becoming visible”)o “Extremal market environment”


2: Theoretical background A simple example [1]

Take a very simple financial product, that is an equity linked note promising to pay a participation to the increase in some stock market index in five years.

The replicating portfolio of the product is made up by: o A zero coupon bond paying the Libor with five years maturity o A zero coupon bond paying the credit risk spread of the issuer with five years

maturity o An equity option with five years exercise time

The main sources of valuation uncertainty are the following. o The calibration of the five year zero coupon Libor, using fixed income market

data and bootstrapping techniques. This valuation problem is common to other fixed income products.

o The calibration of the five year zero coupon credit spread, using the issuer’s or comparable CDS and bond data, and bootstrapping techniques.

o The calibration of the five year equity volatility, using equity options’ market data and bootstrapping techniques. Typically, exchange traded or OTC derivatives do not have a liquid market for 5 years maturity and we must extend implied volatility beyond the traded maturities.


2: Theoretical background A simple example [2]

There are actually other risk sources, mostly the correlations among the risk factors involved.

o Correlation between equity and bondsIt could seem that this should not affect the pricing problem, since it is made under the Forward Martingale Measure (FMM), but the volatility of the forward price depends on correlation.

o Correlation between underlying asset and volatilityThis is relevant in cases in which the underlying asset and its volatility co-move in directions leading to a decrease of the embedded option. This is not the case of this product, which is long both in the underlying asset and its volatility, while the equity market and volatility are known to be negatively correlated.

o Correlation between the embedded option and the credit quality of the issuerActually the embedded option is a vulnerable option whose value is affected by the positive correlation between the exposure (the exercise of the option) and the default probability of the issuer.


2: Theoretical backgroundIncomplete markets: definition

Complete markets are defined by all financial products being “attainable”. This meansthat the payoff of every financial contract or product can be exactly replicated by sometrading strategy. This implies lack of frictions and continuous rebalancing of thereplicating portfolio. Markets are assumed to be perfectly liquid and trading iscostless.

If markets are complete, there exists a unique Equivalent Martingale Measure (EMM)such that the price of each and every asset can be computed by the expected valueunder such measure, and discounted with the risk-free rate. With complete marketsthe price of each financial product would be unique, and there would be no valuationuncertainty problem.

Real world markets are incomplete and there exists a valuation uncertainty problem.The reason is that no perfect hedge exists. More precisely, the reasons for incompletemarkets are:o there are not enough assets to hedge all possible risk factors (no enough Arrow-

Debreu prices);o replicating portfolios cannot be rebalanced in continuous time in such a way as to

allow for a perfect hedge;o there is not enough liquidity in the market, particularly in stress times, to allow

rebalancing of the replicating portfolios.


2: Theoretical backgroundIncomplete markets: theory

From a technical point of view, selecting a price in incomplete markets amounts tochoose a probability measure (pricing kernel) in a set of probability measures. This set contains the probabilities such that the price of each product is a martingale. Thisimplies that for each product it is not possible to find a replicating strategy that attainsthe product for sure.

𝑉𝑄 𝑡 = 𝔼𝑄 𝐷(𝑡, 𝑇)𝑉(𝑇)ȁ𝑄 ∈ ℘

The problem is then to define: the set of probabilities including all the risk-neutral probabilities; a strategy to select a probability in the set.

Notice that the problem of selecting a probability amounts to selecting a lottery. So, apossible strategy to select a specific probability is to use expected utility or some of itsextensions.

Hedging error: every probability measure that is chosen is subjected to hedging error.Based on this, for example, one could select the probability with the lowest hedgingvariance, in the set with some expected hedging cost.


2: Theoretical backgroundIncomplete markets: back to expected utility

We remind that expected utility ranks lotteries by the expected value of a function ofthe pay-off. The function weighting the pay-off is increasing and concave (for risk-averse decision makers) and is called utility function. So, lottery A is preferred tolottery B if

E(U(A)) > E(U(B))with U(x) the utility function.

Ellsberg paradox: what happens if the probability of some lottery is not known forsure? If there is a preference for the lottery whose probability is known, or for theother, the expected utility does not work.

Example: there are 90 balls in an urn, we know that 30 are Red, and the others areBlue or Green. Do you have any preference between:

A lottery paying a premium if the ball is Red A lottery paying a premium if the ball is Blue

Now consider the choice between: A lottery paying a premium if the ball is Blue or Green A lottery paying a premium if the ball is Red or Green

If you have preferences of Red over Blue, then Prob(Red) = 1/3 > Prob(Blue), byconsistently: Prob(Red Green) < Prob(Blue Green) = 2/3 and Prob(Blue) > 1/3


2: Theoretical backgroundIncomplete markets: non-additive expected utility

Notice that the problem with expected utility is additivity. In fact, since additivity meansProb(A B) = P(A) + P(B), for A and B disjoint, we have

Probl(Red) + Prob (Green) > Prob(Blue) + Prob(Green)

which implies Prob(Red) > Prob(Blue).

This implies that allowing for the preferences in the two lotteries to be represented bythe same measure one has to break down additivity.

Non additive representations of preferences are called capacities. These measuresare monotone and are not required to be additive. The expected value with respect tocapacities is represented by the Choquet integral.

There is a duality relationship between sub and super additive capacities andbetween lower and upper Choquet integrals. The duality reminds of the Dempster-Shafer theory.

We will see that this representation is important to represent the set of probabilitymeasures.


2: Theoretical backgroundAlternative theories for price bounds

There are two different approaches to address valuation uncertainty. In both cases theprice bounds are obtained by assuming interval valuation.

Uncertain Volatility Model Volatility is assumed be included in a given interval This leads to two conservative pricing bounds (BSB PDE functions) Avellaneda, Levy and Paràs (1996), AMF

Choquet pricing Interval probabilities (MMEU, Gilboa and Schmeidler, 1989) Conservative valuation (Choquet integral) Cherubini (1997) AMF, Cherubini and Della Lunga (2001) AMF

AMF = Applied Mathematical Finance

MMEU: assume the worst possible probability scenario and select the choice that yields the maximum expected utility.


2: Theoretical backgroundUncertain Volatility Model

Set the delta-neutral portfolio

Volatility choice

The Black-Scholes formula becomes non linear (Black-Scholes-Baremblatt)

where

arg min𝜎𝑚𝑖𝑛≤𝜎≤𝜎𝑚𝑎𝑥

1

2𝜎2𝑆2

𝜕2𝑔

𝜕𝑆2=

𝜎𝑚𝑖𝑛, 𝑖𝑓𝜕2𝑔

𝜕𝑆2> 0,

𝜎𝑚𝑎𝑥, 𝑖𝑓𝜕2𝑔

𝜕𝑆2< 0.

min𝜎𝑚𝑖𝑛≤𝜎≤𝜎𝑚𝑎𝑥

𝑑Π =𝜕𝑔

𝜕𝑡+1

2𝜎2𝑆2

𝜕2𝑔

𝜕𝑆2𝑑𝑡 = 𝑟Π = 𝑟 𝑔 − 𝑆

𝜕𝑔

𝜕𝑆.

𝜎2𝜕2𝑔

𝜕𝑆2

+

: =𝜎𝑚𝑖𝑛2 , 𝑖𝑓

𝜕2𝑔

𝜕𝑆2> 0,

𝜎𝑚𝑎𝑥2 , 𝑖𝑓

𝜕2𝑔

𝜕𝑆2< 0.

𝜕𝑔

𝜕𝑡+

1

2𝜎2

𝜕2𝑔

𝜕𝑆2

+

𝑆2𝜕2𝑔

𝜕𝑆2+ 𝑟𝑆

𝜕𝑔

𝜕𝑆− 𝑟𝑔 = 0,


2: Theoretical backgroundChoquet pricing

Long and short positions

Long and short positions are represented by Choquet integrals with respect tocapacities.

Given a function f and a non-additive measure 𝑄𝑠𝑢𝑏, the upper and lower Choquetintegrals are defined as

𝑉𝑄 𝑡 =

min𝑄∈℘

න𝐷 𝑡, 𝑇 𝑔 𝑆, 𝑇 𝑑𝑄 , long position,

max𝑄∈℘

න𝐷 𝑡, 𝑇 𝑔 𝑆, 𝑇 𝑑𝑄 , short position.

න

−∞

0

𝑄𝑠𝑢𝑏 𝑓 ≤ 𝑥 𝑑𝑥 + න

0

+∞

1 − 𝑄𝑠𝑢𝑏 𝑓 ≤ 𝑥 𝑑𝑥 , lower Choquet integral,

න

−∞

0

1 − 𝑄𝑠𝑢𝑏 𝑓 ≥ 𝑥 𝑑𝑥 + න

0

+∞

𝑄𝑠𝑢𝑏 𝑓 ≥ 𝑥 𝑑𝑥 upper Choquet integral.


2: Theoretical backgroundChoquet pricing

Assume the Breeden and Litzenberger representation of the pricing kernel and thecorresponding call and put prices. According to Breeden and Litzenberger theprobability of exercise of an option can be recovered from the derivative of the optionwith respect to the strike price.

By integrating the pricing kernel we can then recover the prices of call and put optionsas a function of the integral of cumulative distributions, that is, as Choquet integrals,

−1

𝑃 𝑡, 𝑇

𝜕𝐶𝑎𝑙𝑙

𝜕𝐾= 𝑄 𝑆 𝑇 > 𝐾 , ⇒ 𝐶𝑎𝑙𝑙 𝑡 = 𝑃(𝑡, 𝑇) න

𝐾

+∞

)1 − 𝑄(𝑥 𝑑𝑥 ,

1

𝑃 𝑡, 𝑇

𝜕𝑃𝑢𝑡

𝜕𝐾= 𝑄 𝑆 𝑇 ≤ 𝐾 ⇒ 𝑃𝑢𝑡 𝑡 = 𝑃(𝑡, 𝑇) න

−∞

𝐾

𝑄(𝑥)𝑑𝑥 .


2: Theoretical backgroundExamples of valuation uncertainty

Derivatives with counterparty riskCVA and DVA with correlation between the underlying asset and the credit risk of the counterparty (wrong way risk)

Toxic assetsExample: a senior tranche, with high attachment, of a securitization deal traded on the market at much lower value.

Correlation productsthat is Breeden and Litzenberger representation of the pricing kernel and the corresponding call and put prices. Example: options on baskets.

Illiquid derivatives with concentration riskLarge derivative positions require large positions of the underlying asset for delta hedging. Example: large plain vanilla calls/puts on funds.


2: Theoretical backgroundCVA valuation

Assume that the payment schedule of a swap be {t1, t2,…, tn} and that default of the

counterparty receiving fixed rate (B) occurred between tj-1 and tj. In this case the loss

suffered by the surviving counterparty A will be

where sr is the swap rate at the date of default and k is that at the origin.

By the same token, the loss suffered by B due to default of A will be

1-n

ji

1A 0,,max,Lgd nji ttsrkttP

1-n

ji

1B 0,,max,Lgd kttsrttP nji


2: Theoretical backgroundCVA valuation with copula function

Denote GB(tj) the survival probability of party B beyond time tj. Then, the default

probability between time tj - 1 and time tj is GB(tj-1) – GB(tj). Moreover, assume C(u,v)

to be a copula function, and Q(x) the pricing kernel of the swap rate

Then the CVA for counterparty A will be

1

11 ,1,n

ji K

jBjBiB dtGtGQCttPLgd


2: Theoretical backgroundCVA valuation with wrong way risk

Now assume perfect dependence between the underlying asset and default of the

counterparty. In this case, we have the Fréchet bound 𝒞 𝑥, 𝑦 ≤ 𝑀𝑖𝑛 𝑥; 𝑦 .

In this case, the CVA can be computed in closed form as

CVA = LgdBmax[k*(tj) – k,0]A(t, tj, tn) [GB(tj-1) – GB(tj)]

– LgdB PayerSwaption(.;max(k*(tj),k))

where k*(tj) is defined from Q((sr(tj,tn) > k*(tj)) = GB(tj-1) – GB(tj), and

is the swap annuity.

𝐴(𝑡; 𝑡𝑗 , 𝑡𝑛) =

𝑖=𝑗

𝑛−1

𝑃 𝑡, 𝑡𝑖−1 𝜏𝑖


2: Theoretical backgroundCVA valuation with wrong way risk

o For the short end of the contract the worst scenario is perfect negative dependence

between the underlying asset and default of the counter party. In this case, we have

the Fréchet bound 𝒞 𝑥, 𝑦 > 𝑀𝑖𝑛 𝑥 + 𝑦 − 1; 0 .

In this case, the CVA can be computed in closed form as

CVA = LgdA[ReceiverSwaption(.;min(k*(tj),k)) – Receiver swaption(.;k)]

+ LGDA max[k – k*(tj),0](1 – GA(tj – 1) – GA(tj))


2: Theoretical backgroundCVA valuation with wrong way risk (long party)

Vulnerable Call Swaptions: Financial Institution Paying Fixed

0

0,002

0,004

0,006

0,008

0,01

0,012

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Independence

Perfect positive dependence


2: Theoretical backgroundCVA valuation with wrong way risk (short party)

Vulnerable Put Swaptions: Financial Institution Receiving Fixed

0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Independence

Perfect Negative Dependence


2: Theoretical backgroundTranche senior

Assume a senior tranche with attachment equal to 30%, so that it begins to absorblosses only from 30% of collateral on.

Assume a standard valuation model such as Vasicek asymptotic model, that is basedon the assumption that all exposures in the basket have the same default probabilityP and the same asset correlation with systemic risk.

Then, the expected loss of a senior tranche with attachment 𝐿𝑑 is

𝐸𝐿 = 𝑃 − 𝑁 𝑁−1 𝑃 ,𝑁−1 𝐿𝑑 , 1 − 𝜌2

where 𝑁 𝑁−1 𝑥 ,𝑁−1 𝑦 , 𝜌 is the Gaussian copula function.

Now notice that by considering the two extreme values of the copula function𝒞 𝑥, 𝑦 = 𝑥𝑦 and 𝒞 𝑥, 𝑦 = min(𝑥, 𝑦) yields extreme values for the expected losses ofthe senior tranche.


2: Theoretical backgroundTranche senior: pricing bounds

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Rho = 0

Rho = 1


2: Theoretical backgroundRainbow options

Assume a call option on the minimum of a set of assets (Everest). This can be pricedwith a Choquet integral using the copula as the Choquet integral

From the point of view of the issuer, we can compute the conservative value in closedform, for a bivariate product

dTSQTSQTSQCTtP

TKSSSCall

KN

N

))((),...)((),)((,

),),,...,(min(

21

21

)*,max(;,

;,*;,

,,

2

11*

*],max[

2

*

11* 2

KKtSC

KtSCKtSC

dSQTtPdSQTtPC

KK

KK

K

K

KK

1

1


2: Theoretical backgroundDynamic replication of illiquid derivatives

Now assume you are trading a derivative with a costumer, maybe for a large quantityof the underlying asset (concentration risk) or for an illiquid underlying. In this case,standard textbook references for the pricing of options do not apply, since theproduction process of the derivative has an impact on the underlying asset.

Here the only process is to start with a dynamics of the underlying asset and to try areplication strategy, allowing for the liquidity cost of rebalancing the portfolio, and thefunding cost of changing the leverage position. So, the market price incorporatesliquidity costs, both in the sens of market liquidity and funding liquidity. Both thesources of cost are all the more relevant the larger the size of the position.

The problem of finding an optimal trade-off between liquidity cost and liquidity risk isextremely involved. In fact, it requires to define trading strategies: how many times torebalance, when, whether at fixed intervals or contingent on some rule.

The problem is magnified by the need to specify the market impact function, thatincludes:

Which is the trade off between the market impact due to sudden rebalancetrades versus the volatility risk to which one is exposed for partitioned unwinding

How much of the market impact is temporary and how much is permanent.Permanent impacts make the problem particularly involved.


Summary

3. Regulationo Overviewo The Capital Requirement Regulation 575/2013o The EBA Regulatory Technical Standardso AVAs vs XVAso Prudent valuation reportingo Prudent valuation data


3: Regulation Overview

Articles 34 and 105 of Capital Requirements Regulation (CRR, n. 575/2013), in forcesince 1 January 2014, require financial institutions to apply prudent valuation to all fairvalue positions (included positions outside the trading book), setting a new prudentialrequisite for regulatory capital including valuation uncertainty.

The difference between the prudent value and the fair value, accounted in theinstitution’s balance sheet, is called “Additional Valuation Adjustment” (AVA), and isdirectly deducted from the Core Equity Tier 1 (CET1) capital.

Following the CRR, the EBA published a Discussion Paper (EBA/DP/2012/03), aConsultation Paper (EBA/CP/2013/28), and a Final Draft (EBA/RTS/2014/06), to beapproved by the EU Commission, setting the Regulatory Technical Standards (RTS)for prudent valuation.

The EBA Final Draft defines the AVA calculation methodology using two alternativeapproaches, named Simplified Approach and Core Approach. The Final Draft setsalso the requirements on systems, controls and documentation that should supportthe prudent valuation process.

Acronyms: CRR, AVA, CET1, EBA, RTS, EU, Keywords: fair/prudent value, simplified/core approach


Market Data

Models

Estimates

Fair Value accounting AVA

(Additional Valuation

Adjustment)

IFRS 13

Prudent valuation

Prudent value

Deducted from Common

Equity Tier 1 capital

CRR article 105 requisites

Policies &

procedures

Control

systems

Prudent

valuation

principles

3: Regulation CRR 575/2013 [1/8]



Art. 34Prudent valuation

scope

Systems and

controls

Valuation

Valuation

adjustments

Art. 105

CRR

575/2013

CRR Prudent Valuation Tree

Prudent valuation

principles

Degree of certainty, art. 105.1

S&C requirements, art. 105.2

Revaluation frequency art. 105.3

Mark to market, art. 105.4-5

Mark to model, art. 105.6-7

IPV, art. 105.8

Valuation adjustments, art. 105.9-10

Illiquid positions, art. 105.11

Other valuation adj., art. 105.12

Complex products, art. 105.13


CRR art. 34: scope and target

o Scope: all assets measured at fair value

o Target: CET1 capital (not P&L)



CRR art. 105.1, scope and degree of certainty: all positions are subject to prudent

valuation, achieving an appropriate degree of certainty with regard to:

o the dynamic nature of the positions,

o the demands of prudential soundness, and

o the mode of operation and purpose of capital requirements in respect of trading book

positions.

CRR art 105.2, systems and controls: institutions establish and maintain systems and

controls to ensure prudent and reliable valuations, including at least.o Documented policies and procedures for the valuation process, including:

• clearly defined responsibilities of the various areas involved in the determination of the

valuation,

• sources of market information and review of their reliability,

• guidelines for the use of unobservable inputs that reflect the assumptions of authority on

the elements used by market participants to determine the price of the position,

• frequency of independent valuation,

• timing of closing prices,

• procedures for the correction of assessments,

• procedures for the reconciliation of month end and ad hoc.

o Clear and independent (of the front office) reporting lines for the department in charge of the

valuation process.



CRR art 105.3, revaluation frequency: institutions revalue trading book positions at

least daily

CRR art 105.4-5, mark to market: institutions mark their positions to market whenever

possible, using the more prudent side of bid and offer unless they can close out at mid

market.

CRR art 105.6, mark to model: where marking to market is not possible, institutions

must conservatively mark to model their positions and portfolios.



CRR art 105.7, mark to model: o senior management must be aware of the fair-valued positions marked to model and must

understand the materiality of the uncertainty of the risk/performance of the business;

o source market inputs, where possible, in line with market prices, and assess the

appropriateness of market inputs and model parameters on a frequent basis;

o use valuation methodologies which are accepted market practice;

o where the model is developed by the institution itself, it must be based on appropriate

assumptions, assessed and challenged by suitably qualified parties independent of the

development process;

o have in place formal change control procedures, hold a secure copy of the model and use

it periodically to check valuations;

o risk management must be aware of the weaknesses of the models used and how best to

reflect those in the valuation output;

o models are subject to periodic review to determine the accuracy of their performance,

including assessment of the continued appropriateness of assumptions, analysis of profit

and loss versus risk factors, and comparison of actual close out values to model outputs;

o the model must be developed or approved independently

of the trading desk and independently tested, including

validation of the mathematics, assumptions and software

implementation.


Very detailed article

regarding valuation

in general


CRR art. 105.8, independent price verification (IPV): institutions perform independent

price verification in addition to daily marking to market/model. Verification of market

prices and model inputs must be performed by unit independent from units that benefit

from the trading book, at least monthly, or more frequently depending on the nature of

the market or trading activity. Where independent pricing sources are not available or

pricing sources are more subjective, prudent measures such as valuation adjustments

may be appropriate.

CRR art 105.9-10: valuation adjustments: institutions establish and maintain

procedures for considering valuation adjustments, and formally consider the following:

unearned credit spreads, close-out costs, operational risks, market price uncertainty,

early termination, investing and funding costs, future administrative costs and, where

relevant, model risk.

CRR art 105.11, illiquid/concentrated positions: Institutions shall establish and

maintain procedures for calculating an adjustment to the current valuation of any less

liquid positions, which can in particular arise from market events or institution-related

situations such as concentrated positions and/or positions for which the originally

intended holding period has been exceeded.



CRR art. 105.12, other valuation adjustments:

institutions must consider whether to apply a valuation adjustment also:

o when using third party valuations,

o when marking to model,

o for less liquid positions, including an ongoing basis review their continued suitability,

o for uncertainty of parameter inputs used by models.

CRR art. 105.13, complex products: institutions must explicitly assess the need for

valuation adjustments to reflect the model risk associated with using:

o a possibly incorrect valuation methodology

o unobservable (and possibly incorrect) calibration parameters in the valuation model.



3: Regulation Fair Value Vs Prudent Value [1]

Fair Value

o Regulation: IFRS13

o Application: balance sheet

o Percentile: 50% (expected

value)

o The price that would be received

to sell an asset or paid to

transfer a liability in an orderly

transaction between market

participants at the measurement

date

o Must include all the factors that

a market participants would use,

acting in their economic best

interest.

o Atoms: single trades.

o Fair value adjustments

o Non-entity specific

Prudent value

o Regulation: CRR/EBA

o Application: CET1

o Percentile: 90%

o Must reflect the exit price at which

the institution can trade within the

capital calculation time horizon.

o Atoms: valuation positions subject

to a specific source of price

unertainty

o Entity specific

o Subject to diversification benefit

(50% weight for MPU, CoCo, MoRi

AVAs)


3: Regulation Fair Value Vs Prudent Value [2]

Why capital and not P&L ?

P&L is accounted under accounting standards

o EU listed companies: use IFRS (International Financial Reporting Standards),

established and maintained by the IASB (International Accounting Standards

Board) see www.ifrs.org

o US listed companies: use GAAP (Generally Accepted Accounting Standards),

established and maintained by the FASB (Financial Accounting Standards Board),

see www.fasb.org

o Convergence towards IFRS is in progress

Both IFRS and GAAP define the fair value as an exit price, not as a prudent price. Fair

value must be fair, not prudent.

Thus, regulators have decided to account for prudent price through capital, instead of

altering the accounting standards.


3: RegulationOverlaps and possible offsets

AVAs have to be deducted by CET1. Hence, possible double counting w.r.t. other capital deductions should be considered.

AVA UCS vs Expected Loss AmountsCRR article 159 states that “Institutions shall subtract the expected loss amounts calculated in accordance with Article 158 (5), (6) and (10) from the general and specific credit risk adjustments and additional value adjustments in accordance with Articles 34 and 110 and other own funds reductions related to these exposures…”. The Credit Risk capital requirements, including the expected loss (EL) amount, are calculated using the higher accounting values, not the AVA adjusted values. As a result, without an adjustment to the capital requirements on those assets, there is a double hit to capital. The AVA UCS offset against EL, in Article 159, is a mitigation that prevents from double hit.

Day One Profit & Loss deductionsSince these are deductions from profit and loss to account for fair value uncertainty, it seems that there exist a double counting with AVAs, and AVAs can be reduced accordingly. See survey.

OthersTo be understood and clarified, possibly with regulators.


3: RegulationEBA RTS: overview

The EBA RTS issued on 23rd Jan. 2015 have been adopted by the EU with Commission

delegated regulation (EU) 2016/101, published on the OJEU on

The RTS set the detailed regulatory technical standards on prudent valuation under

articles 34 and 105 of CRR

The most important feature of the EBA RTS is the distinction between two different

approaches for the implementation of the prudent valuation methodology: the simplified

approach and the core approach.

The choice between the two approaches depends on a threshold on the sum of the

absolute values of fair-valued assets and liabilities. The EBA sets the threshold at EUR

15 billion.

The EBA RTS sets further requirements in terms of documentation (art. 18), systems

and controls (art. 19). These provisions essentially require Institutions to have in place a

two-level internal policy for fair value (Fair Value Policy) and for prudent value (Prudent

Valuation Policy).


3: RegulationEBA RTS: overview

General

provisions

Sec. 1

Core

approach

Sec.3

EBA RTS

Final draft

EBA RTS Prudent Valuation Tree

Simplified

approach

Sec.2

Documentation

systems &

controls

Sec.4

Methodology for AVA, art. 1

Definitions, art. 2

Sources of market data, art. 3

Conditions of application, art. 4

AVA calculation, art. 5

AVA aggregation, art. 6

Overview, fall back, art. 7

General provisions, art. 8

AVA calculation, art. 9-17

Documentation, art. 18

Systems & controls, art. 19

Entry into force, art. 20 AVA OpR, art. 17

AVA EaT, art. 16

AVA FAC, art. 15

AVA CoPo, art. 14

AVA IFC, art. 13

AVA UCS, art. 12

AVA MoRi, art. 11

AVA CoCo, art. 10

AVA MPU, art. 9


3: RegulationEBA RTS: prudent valuation scope [1/9]

General rules

Region of application: since the CRR is an EU directive, prudent valuation applies to

all institutions within EU countries. In case of institution made of a central holding and

one or more subsidiaries, prudent valuation applies to those individual subsidiaries

included in EU countries.

Scope of application: the CRR art. 5, defines the prudent valuation scope as including

all trading book positions. However, the CRR art. 34 requires that institutions apply the

standards of art. 105 to all assets measured at fair value. The combination of the above

CRR articles 34 and 105 implies that the prudent valuation scope includes all fair-valued

positions, regardless of whether they are held in the trading book or banking book.

The positions at fair value held in both trading and banking books are the following:

Assets Liabilities

Financial assets held for trading (HFT) Financial liabilities held for trading (HFT)

Financial assets at fair value Financial liabilities at fair value

Financial assets available for sale (AFS) (for

the portion not subject to prudential filters)



Positions excluded:

o the EBA RTS, art. 4.2 and 8.1, allow Institutions to exclude partially or totally from the

prudent valuation scope those positions for which a change in their accounting fair

value has only a partial or zero impact on Common Equity Tier 1 capital. These

positions must be included in proportion to the impact of the relevant valuation

change on CET1 capital.

o In particular these positions are the following:

1. positions subject to prudential filters,

2. exactly matching, offsetting positions (back to back),

3. positions in hedge accounting.

o Notice that, since the size of the positions above may be relevant, the prudent

valuation scope is the primary driver of the AVA figures.

o How to compute inclusion/exclusion in practice ? See next slides.



1. Positions subject to prudential filers

o Positions subject to prudential filters refer to the "Financial assets available for sale"

(AFS). The inclusion/exclusion of these positions from the prudent valuation scope

of application follows the CRR requirements.

o The exact percentages of partial inclusions follows the transitional provisions that

each local Regulator issued in compliance with the above CRR requirements.

o Partial inclusion means, for instance, that if 40% of fair value gains and losses are

filtered in CET1, the residual 60% of fair value gains and losses are included in the

prudent valuation scope. In case of 100% filter, the position is completely excluded

by prudent valuation.

Position under prudential filters (AFS) Inclusion

Government bonds issued by EU countries 0%

Other debt securities (excluding the EU

government bonds above)

Partial inclusion depending on the sign of

the reserve and on local prescriptions

EquityPartial inclusion depending on the sign of

the reserve and on local prescriptions


Transitional provisions issued by national regulators.


Circolare 285 Banca d’Italia

The applicable percentage following art. 467, par. 3 CRR is:

a) 20% since 1 Jan. 2014 to 31 Dec. 2014

b) 40% since 1 Jan. 2015 to 31 Dec. 2015

c) 60% since 1 Jan. 2016 to 31 Dec. 2016

d) 80% since 1 Jan. 2017 to 31 Dec. 2017

Local

regulation

in Italy

Article 467 CRR

[…] institutions shall include in the calculation of their Common

Equity Tier 1 items only the applicable percentage



Institutions may not include in own funds unrealized gains and losses related to AFS

positions with central administrations.

Circolare 285 Banca d’Italia

The applicable percentage following art. 468, par. 3 CRR is:

a) 100% 1 Jan. 2014 to 31 Dec. 2014

b) 60% since 1 Jan. 2015 to 31 Dec. 2015

c) 40% since 1 Jan. 2016 to 31 Dec. 2016

d) 20% since 1 Jan. 2017 to 31 Dec. 2017

Article 468 CRR

[…] institutions shall remove in the calculation of their Common

Equity Tier 1 items only the applicable percentage

Local

regulation

in Italy



According to Regulation (EU) 2016/445 of the European Central Bank of 14 Mar 2016

(published OJEU on 26 Mar. 2016), art. 14 and 15, the corresponding art. 467 and 468

of CRR (setting prudential filters for AFS positions) are modified such that AFS positions

in EU government Bonds shall no longer subject to 100% filter, but shall be subject to

standard prudential filters holding for other AFS position:

Inclusion of unrealized losses (art. 14 -> art. 467 CRR):

o 60% in [1/1/2016 – 31/12/2016]

o 80% in [1/1/2017 – 31/12/2017]

Exclusion of unrealized gains (art. 15 -> art. 468 CRR):

o 40% in [1/1/2016 – 31/12/2016]

o 20% in [1/1/2017 – 31/12/2017]

First application date: Q4-2016

This regulatory change will change substantially the AVA figures for institutions

with huge positions in EU govies (more or less all banks...).

NEW



2. Exactly matching, offsetting positions (back to back)

o Back to back positions are groups of trades with total null valuation exposure to

market risk factors (interest rates, volatility, etc.), since any variation in the relevant

market valuation inputs generates opposite variations in the value of the trades in

the group, such that the total value is constant. In other words, the group has null

total sensitivity to market risk factors.

o We stress that back to back positions are neutral w.r.t. other risk factors, such as

counterparty defaults, since the trades into the group may be subscribed with

different counterparties.

o From a prudent valuation point of view:

• Simplified approach: 100% exclusion (EBA RTS art. 4.2)

• Core approach: AVAs must be calculated based on the proportion of the

accounting valuation change that impacts CET1 capital (EBA RTS art. 8.1). In

practice:

• AVA MPU, CoCo and MoRi are null,

• AVA UCS, IFC, CoPo, FAC, EaT, OpR must be computed on the total

valuation exposure of the back to back portfolio.



3. Hedge accounting positions

o Hedge accounting positions are characterized by a hedged instrument (e.g. one ore

more securities, loans or mortgages, etc.) and an hedging instrument (e.g. one ore

more interest rate swaps, credit default swaps, etc.).

o The total package of hedged + hedging instruments has, by construction, a reduced

sensitivity to the underlying risk factors.

o From a prudent valuation point of view, all AVAs must be computed on the total

valuation exposure of the hedge accounting portfolio.



Positions subject

to prudential

filters (AFS)

Positions in

hedge

accounting

Positions for which a

change in their

accounting fair value

has only a partial or

zero impact on CET 1

Art. 4.2 and 8.1

EBA RTS Prudent Valuation scope: exclusions

Positions in

back to back

EU Gov. bonds

Other bonds

Equity

General criteria

for exclusionPositions excluded

% of

exclusion

100% until Sept. 16

Partial, phase in

Partial, phase in

Simplified appr.

Partial, residual exposure

of hedged + hedging items

Core appr.

100%

Partial, residual exposure

to UCS, IFC, CoPo, FAC,

EaT, OpR AVAs


3: RegulationEBA RTS: simplified approach

Simplified Approach

(EBA RTS, sec. 2)

Institutions may apply the Simplified Approach if the sum of the absolute value of

fair-valued assets and liabilities is less than EUR15 bn.

The Simplified Approach AVA is given by the 0,1% of the sum of the absolute value

of fair-valued assets and liabilities.

Example of AVA calculation under the simplified approach. Data do not refer to real portfolios.

Below

threshold


3: RegulationEBA RTS: core approach [1/3]

Core Approach (EBA RTS, sec. 3)

Institutions that at individual or consolidated level exceed the EUR15bn threshold must

apply the core approach.

Each AVA is the excess of valuation adjustments required to achieve the identified

prudent value, over any adjustment applied in the institution’s fair value that can be

identified as addressing the same source of valuation uncertainty as the AVA.

Whenever possible, the prudent value of a position is linked to the 90% percentile of its

price distribution. In practice for AVAs i) Market price uncertainty ii) Close-out costs iii)

Unearned credit spreads, the Institutions must compute the prudent value using the

available market data and the 90% target confidence.

Whenever insufficient data exists to construct a plausible range of values, institutions

shall use an expert-based approach using qualitative and quantitative information

available to achieve a 90% level of certainty in the prudent value.

Additional Valuation

Adjustments



Core approach

Additional Valuation Adjustments

Market

Price

Uncertainty

(MPU)

Art. 9

Close Out

Costs

(CoCo)

Art. 10

Model Risk

(MoRi)

Art. 11

Unearned

Credit

Spread

(UCS)

Art. 12

Investing &

Funding

Cost

(IFC)

Art. 13

Concen-

trated

Positions

(CoPo)

Art. 14

Future

Admin

Costs

(FAC)

Art. 15

Early

Termination

(EaT)

Art. 16

Main

AVAs

UCS/IFC

AVAs

Other

AVAs

Operational

Risk

(OpR)

Art. 17

The AVA hierarchy

Market risk factors

50% weights for diversification

Market risk factors

Split onto main AVAs

Non-market risk factors

100% weights, no diversification



Example of AVA calculation and aggregation under the core approach. IFC and UCS AVAs are split into their MPU, CoCo and MoRi components and pre-aggregated to the corresponding AVAs, then the total AVA is obtained from the aggregation of the other seven residual AVAs. In order to show toy but realistic figures, we assumed the principal AVAs equal to 1/7 of the 99% x 0.1% of the total FV under the core approach. AVA OpR has been calculated as for a non-AMA Institution. In the last line, we also add a possible AVA fall-back calculated on the remaining 1% x 0.1% of the total FV.

Above

threshold


3: RegulationEBA RTS: fall-back approach [1/2]

Fall back approach (EBA RTS, art. 7.2.b)

Institutions that exceed the EUR15bn threshold but cannot calculate the core approach

AVAs for certain positions, are allowed to apply a «fall-back approach» (actualy very

capital intensive), and compute AVAs for those positions as the sum of:

100% of the net unrealised profit (NUP)

10% of the notional value in case of derivatives;

25% of the absolute difference between the fair value (FV) and the net unrealised

profit for non-derivatives.

In formulas:

"unrealised profit shall mean the change, where positive, in fair value since trade

inception, determined on a first-in-first-out basis.”

A𝑉𝐴𝑓𝑏 = 100% 𝑁𝑈𝑃+ + 10% 𝑁𝐷𝑒𝑟 + 25% 𝐹𝑉 − 𝑁𝑈𝑃+ 𝑁𝑜𝑛−𝐷𝑒𝑟

𝑁𝑈𝑃+: = 𝑚𝑎𝑥

𝑖=1

𝑁𝑓𝑏

𝑁𝑈𝑃𝑖 , 0 , 𝑁𝐷𝑒𝑟=

𝑖=1

𝑁𝑓𝑏

𝑁𝑖 , 𝐹𝑉 =

𝑖=1

𝑁𝑓𝑏

𝐹𝑉𝑖 .


3: RegulationEBA RTS: fall-back approach [2/2]

Example of AVA calculation under the fall-back approach. We assume to apply the Fall-Back approach to the 1% portion of the previous core portfolio. The net unrealized P&Ls are the 0.1% of the fair values, positive for derivatives and negative for bonds. The notional for derivatives is assumed 10 times the fair value. The AVA Fall-Back is then summed to the remaining 99% of the previous AVA core to obtain the total AVA.


The core approach is mandatory only for institutions above the threshold of €15 bln.

Institutions below the threshold may choose between simplified and core approaches.

Which one is more convenient (generate smaller capital absorption) ?

There is no precise mathematical relation between the simplified and core AVAs.The actual figures depend principally on the actual positions

included in the prudent valuation scope.

3: RegulationSimplified vs core approaches [1/2]


3: RegulationGlobal view of key regulatory concepts

Fair

value

CRR art. 34, 105

EBA RTS

Prudent

value

Scope

90% confidence level

Simplified approach

Mark to market

Mark to model

IPV

Systems

and

controls

Core approach

Expert based

Fall back

Diversification

0.1% Formula

9 AVAs


3: RegulationAVAs vs XVAs

Simple question, difficult answerShould XVAs be included into the prudent valuations scope ?

Let’s look atthe state of the art...

...and try some forecast

XVA Accounting standards Accounting practice

CVA, DVA YES, both IFRS13 and GAAP mention

about counterparty and own credit

risk.

Some news on DVA expected

YES, CVA and DVA are normally included

into accounting fair value and reported in

public balance sheet disclosures

FVA NO, at least not explicitly YES, most banks have included FVA into

accounting fair value and report some

(scarce) information in public balance

sheet disclosures

MVA NO, see recent survey NO, see recent survey and public balance

sheet disclosures

KVA NO, see Kenyon&Kenyon, Risk Mag.

Mar. 2016

NO, see recent survey

xxxVA Who knows...

NEW


Recently, two regulators proposed a consultation on enhancements to the reporting of prudent valuation figures.

The industry (ISDA, IIF, AFME, etc.) is actively discussing the proposed template and comments to BCBS are expected. Main issues are the following:o Partial overlapping and consistency of AVA definitions under BCBS and EBA RTSo Different AVA scopes of applications, since EBA RTS allows for many exclusions.o AVAs break down by asset class is problematic for EU Institutions because EBA RTS

requires AVA calculation at valuation exposure level. For example, AVA MPU for some risk factor (e.g. IR/vols and FX rates/vols) naturally include multiple asset classes.

1. BCBS Consultative Document, “Pillar 3 disclosure requirements –consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016.

Template PV1, in particular, aims to disclose prudent valuation figures under Pillar 3, consistently with previous BCBS requirements:o BCBS “International Convergence of Capital Measurement and

Capital Standards” (Basel 2, comprehensive version) June 2006, paragraphs 698-701.

o BCBS “Supervisory guidance for assessing banks’ financial instrument fair value practices”, April 2009 (in particular Principle 10).

3: RegulationPrudent valuation reporting [1/3]

NEW


Template PV1 proposed in BCBS Consultative Document, “Pillar 3 disclosure requirements – consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016.


NEW


2. EBA consultation paper (EBA/CP/2016/02), ”Draft implementing Technical Standards amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016, issued for comment by 31 March 2016.

The proposed amendement of prudent valuation supervisory reporting is articulated into four new templates.

Template C 32.01: fair valued asset and liabilitieso Rows: accounting categorisation (HFT, AFS, etc.)o Columns: fair value amounts of inclusions and

exclusions according to EBA RTS

Template C 32.02: core approacho Rows: break down by portfolio/trade class (vanilla/exotic), diversification benefit, fall back app.o Columns: AVAs and fair value adjustments according to EBA RTS.

Template C 32.03: focus on AVA MoRi

Template C 32.01: focus on AVA CoPo

Main issues are the following: breakdown by portfolio/trade class (vanilla/exotic) is not consistent with AVA calculation by

valuation exposures, amount of data required


NEW


FV under prudent valuation scope = FV asset & liabilities – FV under prudential filters

3: RegulationPrudent valuation data: QIS [1/3]


The EBA conducted a QIS to estimate the total impact of the requirements of the RTSincluding 59 banks across 15 jurisdictions, with the following results.

Small banks: < 15 €/bln Medium banks: 15 - 100 €/bln Large banks: > 100 €/bln

Average

227 €/mln

per bank

3: Regulation Prudent valuation data: QIS [2/3]


According to EBA: [*]

approximately 6,500 credit institutions across EEA Member States (as of 2013) reportsupervisory data to their respective competent authorities.

Total value of assets: approximately EUR 42,000 billion.

Approximately 750 institutions (11%) are above the EUR 15 billion threshold.

[*] European Banking Authority, Consultation Paper, “Draft Implementing Technical Standards amendingCommission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016,https://www.eba.europa.eu/-/eba-seeks-comments-on-reporting-of-prudent-valuation-

information

3: Regulation Prudent valuation data: QIS [3/3]


3: RegulationPrudent valuation data: 2014-2015 [1/3]

Source: elaboration of public data (in collaboration with Ernst Young).

NEW



Source: elaboration of public data (in collaboration with Ernst Young).

NEW


Comments

Fair value is given by FV assets + FV liablities includingo Held for trading (HFT)o Fair Value Option (FVO)o Hedging Derivatives (HD)o Available For Sale (AFS)

Fair value for prudent valuation has been estimated from fair value excluding HD and AFS (100%, no AFS filters applied, slightly underestimated).

AVA/CET1 figures are rather different, ranging from negligible to important %.

AVA core / AVA simplified > 1 in a few cases, thus AVA simplified is neither an AVA cap nor an AVA floor.

Prudent valuation not driven by L3 instruments: moving from AVA/L3 to AVA /(L2+L3) changes the figures by a factor of 100.

2014-2015 average AVAs double the 2013 QIS result (500 vs 227 mln€).


NEW


1. XVAs

3: RegulationPrudent valuation data: survey [1/4]

Restricted access to clients only Dec.2015 30 respondents (18 GSIBs, 15 UK) 60 questions EBA RTS not yet in place at the time

One third does not account FVA in fair value, more than half does account AVA IFC in prudent value.

MVA and KVA are not accounted both in fair and prudent values.

NEW


1. XVAs (cont’d)


Only 30% use a spread term structure

«Peer estimate» is a possible answer to the question «what is an exit price for FVA ?»

Possible use of Markit XVA service

Both funding spreads sources and term structures vary considerably, both for FVA (Fair Value) and for AVA IFC (prudent value)

NEW


2. P&L variance test


The P&L variance test is difficult to run and pass in case of many relevant risk factors, and may lead to huge AVA MPU.

60% ignore the P&Lvariance test

Only 7% run extensive application

Only 14% apply with quarterly frequency

NEW


3. Other


One half does apply/does not apply offsetting between AVAs and other regulatory capital reserves.

Possible offsets should be clarified, to avoid possible capital double countings.

One third reduces the valuation exposure.

NEW


4. AVA calculationo Definitions and basic assumptionso Market price uncertainty AVAo Close-out costs AVAo Model risk AVAo Unearned credit spreads AVAo Investing and funding costs AVAo Concentrated positions AVAo Future administrative costs AVAo Early termination AVAo Operational risk AVAo Case studies & examples

Summary


4: AVA calculationDefinitions and basic assumptions [1]

In other words, a valuation position will display valuation exposures to its valuation inputs. Clearly the degree of valuation exposure to a valuation input depends on the particular valuation position.

Definitions (EBA RTS art. 2)

Item Definition Example

Valuation

position

A portfolio of financial instruments or

commodities measured at fair value, held in

both trading and non-trading books

E.g. a portfolio of

derivatives

Valuation

input

A set of parameters (observable or non-

observable) that influences the fair value of a

valuation position

E.g. yield curve,volatility

cube, market/historical

correlations, prepayment,

etc.

Valuation

exposure

The amount of a valuation position which is

sensitive to the change in a valuation input

E.g. the trades in portfolio

above sensible to the

valuation inputs above.



Fair value

In general, we denote the fair value of a valuation position 𝑝𝑖 at time t with 𝐹𝑉 𝑡, 𝑝𝑖 or, shortly, with 𝐹𝑉𝑖 𝑡 , with 𝑖 = 1,… , 𝑁𝑝. Given a set of valuation positions subject to

prudent valuation, we denote the total fair value as

𝐹𝑉 𝑡 =

𝑖=1

𝑁𝑝

𝐹𝑉𝑖 𝑡

In the context of prudent valuation, we consider the following properties of fair value FV. FV is positive for assets (𝐹𝑉𝑖 𝑡 > 0) and negative for liabilities (𝐹𝑉𝑖 𝑡 < 0). Financial institutions have appropriate internal IPV process in place (EBA RTS, p. 7). FV is computed by the institution consistently with the applicable financial reporting

standards, e.g. IFRS13, and with its internal fair value policy. The institution possibly applies and reports a number of valuation adjustments to the

FV, according to its internal fair value policy.



Fair value (cont’d)

The FV of a valuation position may be subject to the sources of uncertainty mentioned in the CRR, art. 105.10-11, and thus associated to a specific AVA under the core approach described in the EBA RTS.

According to EBA RTS art. 8.3, the FV of a valuation position associated to a specific AVA under the core approach must include all the fair value adjustments possibly applied by the institution associated to the same source of valuation uncertainty as the specific AVA. In case a fair value adjustment cannot be associated to the same source of valuation uncertainty of a specific AVA, it must not be included in the FV for the specific AVA calculation. In case of impossible association with any AVA, the fair value adjustment cannot be included at all in the prudent valuations scope.




Fair value for derivativesIn general, we may consider the fair value for derivatives split into various components,

𝐹𝑉 𝑡 = 𝑉0 𝑡 + 𝑉𝐴𝑑𝑗 𝑡

𝑉𝐴𝑑𝑗 𝑡 = 𝑉𝑏𝐶𝑉𝐴 𝑡 + 𝑉𝐹𝑉𝐴 𝑡 + 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 + 𝑉𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 + ⋯

where o 𝑉0 𝑡 is the “base” fair value component at valuation time t, as if the contract were

covered by a perfect CSA;o the other components gathered in 𝑉𝐴𝑑𝑗 𝑡 corresponds to the value of the various

risk components underlying the financial instrument, such as the bilateral counterparty risk 𝑉𝑏𝐶𝑉𝐴 𝑡 , funding risk 𝑉𝐹𝑉𝐴 𝑡 , bid-ask 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 , model risk 𝑉𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 , etc. Such components may be considered or not in the FV or in in 𝑉𝐴𝑑𝑗 𝑡 according to the fair value policy of the institution.




Fair value for securitiesWe consider the fair value for securities, instead, as a single value, without splitting into distinct components. In other words, the value of the various risk components is included in the credit spread associated to the security.



Valuation input

The FV of a valuation position 𝑝𝑖 depends on its valuation inputs, denoted with 𝑢𝑗 , 𝑗 = 1, … , 𝑁𝑢,

The FV may be also denoted as 𝐹𝑉(𝑡, 𝑝𝑖 , 𝑢1, … , 𝑢𝑁𝑢). We stress that different

valuation positions depend, in general, on different valuation inputs.

The valuation input 𝑢𝑗 is associated to a single elementary risk factor, or source of

valuation uncertainty.



Valuation exposure

The valuation exposure of a valuation position 𝑝𝑖 to the valuation input 𝑢𝑗 is the

amount of that valuation position which is sensitive to the change in the valuation input 𝑢𝑗.

The valuation exposure can be also associated to the sensitivity of the valuation position 𝑝𝑖 to the valuation input 𝑢𝑗.

In a wider sense, the valuation exposure is anything that measures the dependency of the FV of the valuation position 𝑝𝑖 to the valuation input 𝑢𝑗.



Prudent value

We denote the prudent value of category k for a valuation position 𝑝𝑖 associated to the source of valuation uncertainty 𝑢𝑗 at time t with 𝑃𝑉 (𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘) or, shortly, with

𝑃𝑉𝑖𝑗𝑘 𝑡 , with 𝑗 = 1,… , 𝑁𝑢 and 𝑘 = 1,… ,𝑁𝐴𝑉𝐴. The category is the AVA type (MPU,

CoCo, etc…).

Degree of certaintyThe CRR (article 105.1) requires a prudent value that achieves an “… appropriate degree of certainty”. The EBA RTS specifies the appropriate degree of certainty as follows.

o AVA MPU, CoCo e MoRi (art. 9-11):• where possible, the prudent value of a position is linked to a range of

plausible values and a specified target level of certainty (90%);• in all other cases, an expert-based approach is allowed, using qualitative

and quantitative information available to achieve an equivalent level of certainty as above (90%).

o AVA UCS and IFC (art. 12-13): these AVAs must be split into their MPU, CoCoand MoRi components, and aggregated to the corresponding MPU, CoCo and MoRi AVAs, respectively. Thus, the same level of certainty in the prudent value (90%) must be statistically achieved.



Prudent value (cont’d)

o Other AVAs (CoPo, FAC, ET, OpR, art. 14-17): it must be statistically achieved the same level of certainty in the prudent value (90%) as for the previous AVAs (art. 8.3).

o For positions where there is valuation uncertainty but it is not possible to statistically achieve a specified level of certainty, the same target degree of certainty in the prudent value (90%) is required.

o “The EBA accepts that for the majority of positions where there is valuation uncertainty, it is not possible to statistically achieve a specified level of certainty; however, specifying a target level is believed to be the most appropriate way to achieve greater consistency in the interpretation of a “prudent’ value”.”

In conclusion, the same degree of certainty in the prudent value (90%) must be achieved for all AVAs.



Prudent value (cont’d)

o Notice that, by definition, the prudent value is always equal to or lower than the fair value, both for assets and liabilities. Taking into account the FV definition above we have, for both assets and liabilities,

𝑃𝑉𝑖𝑗𝑘 𝑡 ≤ 𝐹𝑉𝑖 𝑡 ∀ 𝑖 = 1, … , 𝑁𝑝, 𝑗 = 1, … , 𝑁𝑢, 𝑘 = 1,… , 𝑁𝐴𝑉𝐴

o Hence, PV is generally positive for assets (𝑃𝑉𝑖𝑗𝑘 𝑡 > 0) and negative for

liabilities (𝑃𝑉𝑖𝑗𝑘 𝑡 < 0). This is not strictly true in all cases, since some asset

(e.g. an OTC swap) may have positive FV and negative PV (not viceversa).



Additional Valuation Adjustment (AVA)

Simplified approachGiven the total fair value of assets and liabilities, 𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 𝑡 > 0, 𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑡 < 0, the total AVA under the simplified approach is given by the following expression

𝐴𝑉𝐴 𝑡 = 0.1% × 𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 + 𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠

where

𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 ≔

𝑖=1

𝑁𝐴𝑠𝑠𝑒𝑡𝑠

𝐹𝑉𝑖 𝑡 ,

𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 ≔

𝑖=1

𝑁𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠

𝐹𝑉𝑖 𝑡 .



Additional Valuation Adjustment (AVA) (cont’d)

Core approachGiven the fair value of a valuation position 𝑝𝑖, 𝐹𝑉𝑖 𝑡 , and the corresponding prudent value of category k associated to the source of valuation uncertainty 𝑢𝑗, 𝑃𝑉𝑖𝑗𝑘 𝑡 , the

AVA under the core approach is given by the following expressions

𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 : = 𝑤𝑘 𝐹𝑉 𝑡, 𝑝𝑖 − 𝑃𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 ,

𝐴𝑉𝐴 𝑡, 𝑘 : =

𝑖=1

𝑁𝑝

𝑗=1

𝑁𝑢

𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 ,

where:o 𝑤𝑘 is the aggregation weight, such that 𝒘 = 0.5,0.5,0.5,1,1,1,1 for the seven

AVAs MPU, CoCo, MoRi, CoPo, FAC, ET, OpR, respectively.

o 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 ≔ 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 is the k-th AVA for valuation position 𝑝𝑖 and source

of valuation uncertainty 𝑢𝑗 at time t, weighted for aggregation;

o 𝐴𝑉𝐴 𝑡, 𝑘 is the total k-th category level AVA associated to all relevant sources of valuation uncertainty 𝑢1, … , 𝑢𝑁𝑢 and valuation positions 𝑝1, … , 𝑝𝑁𝑝. Also this AVA is

already weighted for aggregation by construction of 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 .




Notice that:

𝐴𝑉𝐴𝑘 𝑡 always include the aggregation weight 𝑤𝑘 at any level (valuation exposure, total AVA, total PVA);

𝐴𝑉𝐴𝑘 𝑡 ≥ 0 ∀ 𝑘 at any level (valuation exposure, total AVA, total PVA), both pre and post aggregation;

𝐴𝑉𝐴𝑘 𝑡 = 0 when the fair value is already prudent w.r.t. the 𝐴𝑉𝐴𝑗 source of valuation

uncertainty, 𝐹𝑉𝑖 𝑡 = 𝑃𝑉𝑖𝑗𝑘 𝑡 ;

the previous expressions holds both for assets (𝐹𝑉i 𝑡 > 0) and liabilities (𝐹𝑉i 𝑡 <0).




AVA for derivatives

Remind that for derivatives the total value may be split across different components

𝐹𝑉 𝑡 = 𝑉0 𝑡 + 𝑉𝐴𝑑𝑗 𝑡

𝑉𝐴𝑑𝑗 𝑡 = 𝑉𝑏𝐶𝑉𝐴 𝑡 + 𝑉𝐹𝑉𝐴 𝑡 + 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 + 𝑉𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 + ⋯

We assume that such components are not strongly correlated. In particular, we assume that the market value is not strongly correlated with credit and funding risk.

In this case, also the AVAs results to be split across the same components

𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 = 𝐴𝑃𝑉𝐴0 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝑘 + 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝐶𝑉𝐴 + 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖 , 𝑢𝑗 , 𝐹𝑉𝐴 +⋯



Prudent Valuation Adjustment (PVA)

The total Prudent Valuation Adjustment (PVA), to be deduced from the CET1, is computed as follows.

𝑃𝑉𝐴 𝑡 ≔

𝐴𝑉𝐴(𝑡) Simplified approach,

𝑘=1

𝑁𝐴𝑉𝐴

𝐴𝑉𝐴𝑘 𝑡 Core approach.

The detailed AVA aggregation rules under the core approach are discussed within thedetailed AVA calculation rules in the following.



AVA aggregation

The total AVA under the core approach is computed using the following algorithm.

CoPo, FAC, EaT, OpR AVAs are aggregated each as the sum of its corresponding individual components at valuation positions level, each weighted at 100%.

UCS and IFC AVAs are decomposed each into 3 components related to MPU, CoCoand MoRi uncertainties, which are taken into account in the total MPU, CoCo and MoRi AVA aggregation discussed below.

MPU, CoCo and MoRi AVAS are aggregated each as the sum of:o its individual components at valuation positions levelo the corresponding UCS and IFC AVA contributions above, o all weighted at 50%.

The total AVA is computed as the simple sum of the residual MPU, CoCo, MoRi, CoPo FAC, EaT, OpR AVAs determined above.

In conclusion, the final aggregation includes 50% of MPU, MoRi, CoCo, UCS and IFC AVAs (5 out of 9), and 100% of CoPo FAC, EaT, OpR AVAs (4 out of 9).



Definitions summary

Item Definition Comments

Fair value 𝐹𝑉 𝑡 =

𝑖=1

𝑁𝑝

𝐹𝑉𝑖 𝑡 i = index for valuation positions

Prudent Value𝑃𝑉𝑖𝑗𝑘 𝑡 ≤ 𝐹𝑉𝑖 𝑡

∀ 𝑖 = 1, … , 𝑁𝑝, 𝑗 = 1, … , 𝑁𝑢, ∀ 𝑘 = 1,… , 𝑁𝐴𝑉𝐴

o j = index for risk factors

o k = index for AVAs

Additional

Valuation

Adjustment

(simplified)

𝐴𝑉𝐴 𝑡 = 0.1%

𝑖=1

𝑁𝐴𝑠𝑠𝑒𝑡𝑠

𝐹𝑉𝑖 𝑡 +

𝑖=1

𝑁𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠

𝐹𝑉𝑖 𝑡𝐴𝑉𝐴 𝑡 is the total valuation

adjustment at time t

Additional

Valuation

Adjustment

(core)

𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 ∶= 𝑤𝑘 𝐹𝑉𝑖 𝑡 − 𝑃𝑉𝑖𝑗𝑘 𝑡 ,

𝐴𝑉𝐴𝑘 𝑡 : =

𝑖=1

𝑁𝑝

𝑗=1

𝑁𝑢

𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡

o 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 is the k-th AVA

associated to source of

valuation uncertainty j and

valuation position i at time t,

o 𝐴𝑉𝐴𝑘 𝑡 is the total k-th AVA at t

Prudent

Valuation

Adjustment

𝑃𝑉𝐴 𝑡 ≔

𝐴𝑉𝐴(𝑡) Simplified

𝑘=1

𝑁𝐴𝑉𝐴

𝐴𝑉𝐴𝑘 𝑡 Core

𝑃𝑉𝐴 𝑡 is the total valuation

adjustment at time t


Price distribution, fair value, fair value adjustment, prudent value, AVA

What about realprice distributions...?

Fair value

(mean)Fair value

adjusted

Prudent value

(quantile)

Fair value adjustment

AVA



4: AVA calculationData sources

Market

based

Data sourcing

(EBA RTS Art. 3)

Expert

based

Consensus service data

Proxy data based on similar instruments

Application of prudent shifts to valuation inputs

Exchange prices in a liquid market

Trades in the exact same or very similar instrument,

either from internal records or from the market

Tradable quotes from brokers and other market

participants

Identification of natural bounds to the value of an

instrument

Indicative broker quotes

Counterparty collateral valuations


4: AVA calculationAVA discussion scheme

Since AVAs are rather involved and diversified, we need to discuss each AVA using a fixed scheme, including:

AVA definition and regulatory references AVA scope of application Fair Value related to the AVA AVA calculation scheme Examples Applications


4: AVA calculationAVA Market Price Uncertainty (MPU) [1]

AVA definitionAVA Market Price Uncertainty (MPU) refers to the valuation uncertainty of a valuation exposure arising from uncertainty of a valuation input.

This kind of uncertainty is rather common in price evaluation and may appear in different situations, for example:o when the financial instrument is marked to market (e.g. a bond listed), and there

are multiple reliable price contributors;o when the financial instrument is marked to model using some valuation input (e.g.

an OTC IRS valued using multiple yield curves based on IRS market quotes), and there are multiple price contributors for the valuation inputs (e.g. multiple IRS market makers).

AVA main referenceso EBA RTS, article 9.o EBA FAQs 6.1, 21, 23, 23.1, 28, 30, 31, 40.1, 40.3.



AVA scope of applicationWithin the general prudent valuation scope (see before), AVA MPU regards in particular those valuation positions without either a firm tradable price, or a price that can be determined from reliable data based on a liquid two-way market, and such that at least one valuation input has material valuation uncertainty.

AVA MPU shall be computed for all valuation positions 𝑝𝑖 , 𝑖 = 1, … , 𝑁𝑝 showing a

valuation exposure to a valuation input 𝑢𝑗 , 𝑗 = 1, … , 𝑁𝑢 (valuation exposure level).

We stress that a single valuation position 𝑝𝑖 may show a valuation exposure to either none, or one, or a few, or many, or all valuation inputs 𝑢𝑗. Thus we may have

A𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗1 = 0 and 𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗2 ≠ 0 for the same valuation position

𝑝𝑖 and two different valuation inputs 𝑢𝑗1 ≠ 𝑢𝑗2.

AVA Fair Value The FV of the trades subject to AVA MPU may include or not the effect of possible MPU. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover possible losses related to MPU. In this case the FV subject to prudent valuation for AVA MPU must include these FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA MPU (keeping the AVA non-negative).



Does the valuation position have a valuation

exposure 𝑝𝑖 , 𝑖 = 1,… ,𝑁𝑝, to uncertainty of

valuation inputs 𝑢𝑗 , 𝑗 = 1,… ,𝑁𝑢?

o Is there firm evidence of a tradable price for the valuation

exposure 𝑝𝑖 ?

o Or can the price for the valuation exposure 𝑝𝑖 be determined

from reliable data based on a liquid two-way market (as

defined in art. 338 of CRR) ?

𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 = 0

YES

Compute individual 𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗for each valuation exposure 𝑝𝑖 to

each valuation input 𝑢𝑗

Do sources of market

data indicate no

material valuation

uncertainty ?

YES

YES

NO

NO

AVA Market Price Uncertainty (MPU) (EBA RTS, article 9) refers to the valuation uncertainty of a

valuation exposure arising from uncertainty of a valuation input.

NO

Continue



o Use the data sources defined in Art. 3.

o Calculate AVAs on valuation exposures 𝑝𝑖 related to each valuation input 𝑢𝑗 used in the

relevant valuation model.

o For non-derivative valuation positions, or derivative positions which are marked to market,

refer to the instrument price, or decompose into each valuation input required to calculate

the exit price, treated separately.

o If a valuation input 𝑢𝑗 consists of a (D-dimensional) matrix of parameters, 𝑢𝑗𝛼𝛽𝛾…

, calculate

𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 based on the valuation exposures related to each matrix element 𝑢𝑗𝛼𝛽𝛾…

.

o If a valuation input 𝑢𝑗 does not refer to tradable instruments, map the valuation input and

the related valuation exposure to a set of market tradable instruments.

Do you reduce the number

of parameters of the

valuation input 𝑢𝑗 (D-dim.

matrix) for the purpose of

calculating AVAs ?

ContinueNO

P&L

variance

test

Positive

YES

Negative

Subject to independent

control function review

and internal validation on

at least an annual basis



Estimate a point

ො𝑢𝑗 within the

range with 90%

confidence to exit

the valuation

exposure at that

price or better.

Use expert-based

approach using

qualitative and

quantitative

information

available to achieve

a prudent value ො𝑢𝑗with confidence

level equivalent to

90%.

Do sufficient data exists to

construct a range of

plausible values for a

valuation input 𝑢𝑗?

YES

NO

Notify competent

authorities of the

valuation

exposures for

which this

approach is

applied, and the

methodology used

to determine the

AVA.

Estimate a point

ො𝑢𝑗 within the

range with 90%

confidence that

the mid value that

could be achieved

in exiting the

valuation

exposure would

be at that price or

better.

Continue

Is the range of

plausible values

of 𝑢𝑗 is based on

exit prices ?

Is the range of

plausible values

of 𝑢𝑗 is based on

mid prices ?

NO

YES



Compute individual AVA MPU

𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝑤𝑀𝑃𝑈 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 − 𝑃𝑉𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗

Apply the valuation input uncertainties ො𝑢𝑗 to valuation

exposures 𝑝𝑖 and compute prudent value MPUs

By revaluation:

𝑃𝑉𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝐹𝑉𝑀𝑃𝑈 𝑡, 𝑝𝑖 , ො𝑢𝑗or (when the uncertain input is the

instrument price):

𝑃𝑉𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 = ො𝑢𝑗

By exposure

𝑃𝑉𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 −𝜕𝐹𝑉

𝜕𝑢𝑗ො𝑢𝑗 − 𝑢𝑗

Compute total category level AVA MPU

𝐴𝑉𝐴𝑀𝑃𝑈 𝑡 =

𝑖=1

𝑁𝑝

𝑗=1

𝑁𝑢

𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 , 𝑢𝑗



AVA calculation

o Securities

• Impaired/defaulted securities

𝐴𝑉𝐴𝑀𝑃𝑈 𝑡 = 0 if the FV is already conservative and does not depend on

uncertain market data, otherwise go to next cases.

• Liquid securities accounted at Fair Value Level 1

𝐴𝑉𝐴𝑀𝑃𝑈 𝑡 = 0, if the FV is calculated on market tradable prices with negligible

bid-ask, otherwise go to next cases.

• Contributed securities accounted at Fair Value Level 1

a possible approach is

A𝑉𝐴𝑀𝑃𝑈 𝑡 = 𝑤𝑀𝑃𝑈 ൝+0.9 × 𝐹𝑉 𝑡 − 𝑉𝑏𝑖𝑑

𝑚𝑖𝑛 𝑡 long positions,

−0.9 × 𝐹𝑉 𝑡 − 𝑉𝑎𝑠𝑘𝑚𝑎𝑥 𝑡 short positions.

where 𝑉𝑏𝑖𝑑𝑚𝑖𝑛 𝑡 /𝑉𝑏𝑖𝑑

𝑚𝑖𝑛 𝑡 are the lowest/highest bid/ask prices quoted at time t,

and 𝑤𝑀𝑃𝑈 = 0.5.

• Securities accounted at Fair Value Level 2 or 3

AVA MPU shall be computed via sensitivity or full revaluation based on relevant

risk factors, in particular credit spread and interest rate curves, using prudent

MPUs.



AVA calculation (cont’d)

o Derivatives

AVA MPU is computed via sensitivity or full revaluation based on relevant risk

factors.

MPU estimation

AVA MPU calculation is based on the estimation of MPUs of relevant (possibly all)

risk factors, including volatilities and correlations.

Possible sources of MPUs are the following.

o Front office traders active in their respective markets.

o Appropriate selection of multiple contributors (brokers, market makers) available

from data providers (i.e. Bloomberg or Reuters).

o Consensus price services (e.g. Markit).

o Collateral counterparty valuations for derivatives.

o Historical series of prices and market data



Examples

o Bond for which there exist multiple price contributors.

o IRS valued using multiple yield curves based on market quotations (Fras, Futures, OIS, IRS, Basis IRS, etc.) for which there exist multiple market makers.



Case study of AVA MPU calculation for a security.

• Top left: market bid and ask prices. FV is computed as average mid price = 162.25.

• Bottom left: ranking and percentiles of mid prices, AVA MPU for long and short positions, equal to 0.14 and 0.12, respectively.

• Top right: distribution chart.



Examples with sensitivities.

See EBA RTS sec. 4.1.1 and ref. [23].



P&L variance test

Notation

𝑅𝑖𝑗 , 𝑖 = 1, … , 𝑁𝑅, 𝑗 = 0, … , 𝑁𝑑 = i-th risk factor (scalar, vector or matrix element,

generically indexed by i with some ordering) for j-th date (backward time ordered, j =

0 = today, j = 1 = yesterday business day, etc….).

Δ𝑅𝑖𝑗 ≔ 𝑅𝑖𝑗 − 𝑅𝑖𝑗−1 = j-th daily variation of risk factor 𝑅𝑖𝑗.

𝑉𝑗 = fair value of today’s valuation exposure at j-th date (static portfolio).

𝛿𝑖𝑗 ≔ Τ𝜕𝑉𝑗 𝜕𝑅𝑖𝑗 = first-order sensitivity of today’s valuation exposure to risk factor 𝑅𝑖𝑗(delta, vega, rho, etc.).

Discussion

We know the valuation exposure and its fair value at today’s date, 𝑉0. Instead, it’s much

more difficult to recompute the past fair values of the present valuation exposure,

𝑉1, … , 𝑉𝑁𝑑 . Thus, we approximate such values using first order Taylor expansion and

today’s risk factors sensitivities as follows

𝑉𝑗 ≅ 𝑉𝑗−1 +

𝑖=1

𝑁𝑅

𝛿𝑖𝑗 Δ𝑅𝑖𝑗 +⋯ ≅ 𝑉𝑗−1 +

𝑖=1

𝑁𝑅

𝛿𝑖,0 Δ𝑅𝑖𝑗 .



P&L variance test (cont’d)

Notice that we’re assuming that first order sensitivities are fairly constant w.r.t. the risk

factors levels, 𝛿𝑖,𝑗 ≅ 𝛿𝑖,0 ∀ 𝑗. This is consistent with first order expansion and the static

portfolio assumption. Second order sensitivities (gamma in particular) can be introduced

in the Taylor expansion if required.

Hence we may define the j-th daily profit & loss of the valuation exposure as

𝑃𝐿𝑗: = 𝑉𝑗 − 𝑉𝑗−1 ≅

𝑖=1

𝑁𝑅

𝛿𝑖,0 Δ𝑅𝑖𝑗 , 𝑗 = 1, … , 𝑁𝑑,

and we may compute the variance of the historical series as

𝑉𝑎𝑟 𝑃𝐿 = 𝑉𝑎𝑟 𝑃𝐿1, … , 𝑃𝐿𝑁𝑑 ,

Where the EBA RTS requires 𝑁𝑑 = 100.




The calculations above may refer to both unreduced and reduced sets of risk factors as

well. Denoting reduced quantities with a hat, the reduced set is characterized by a lower

number of risk factors, 𝑁𝑅 < 𝑁𝑅. We may calculate the profit & loss of the reduced

valuation exposure as

𝑃𝐿𝑗: = 𝑉𝑗 − 𝑉𝑗−1 ≅

𝑖=1

𝑁𝑅

መ𝛿𝑖,0 Δ𝑅𝑖𝑗 , 𝑗 = 1, … , 𝑁𝑑,

with the constrain on the total reduced and unreduced sensitivities,

𝑖=1

𝑁𝑅

መ𝛿𝑖,0 =

𝑖=1

𝑁𝑅

𝛿𝑖,0 ,

for each single risk factor class (e.g. delta, vega, etc.).




Finally, the P&L variance ratio test required by EBA RTS [1], art. 9 can be calculated as

𝑃𝐿 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑟𝑎𝑡𝑖𝑜 =𝑉𝑎𝑟 𝑃𝐿 − 𝑃𝐿

𝑉𝑎𝑟 𝑃𝐿≤ 0.1,

where

𝑉𝑎𝑟 𝑃𝐿 − 𝑃𝐿 = 𝑉𝑎𝑟 𝑃𝐿1 − 𝑃𝐿1, … , 𝑃𝐿𝑁𝑑 −𝑃𝐿𝑁𝑑 .

Comments

The approach above is based on common approximations and requires, beyond the

present value and sensitivities of the valuation exposures, just the historical series of

the relevant market risk factors. The most important factor driving the result of the test is

obviously the choice of the reduced valuation exposure and it’s robustness over time.




Possible issues

How to define the unreduced set of risk factors ? -> choose the tradable nodes.

How to choose the reduced set of risk factors ? This is arbitrary: in principle,

institutions are allowed, for each prudent valuation reporting date, to look for the

most convenient level of aggregation that minimizes the AVA and passes the test.

How to ensure test stability from time to time ? The test success/failure strongly

depends on the distribution of the sensitivity w.r.t. the chosen level of aggregation.

Thus the same test applied to a dynamical portfolio may be positive one day and

negative another day.

Facts

Recent experience shows that:

at least for some important cases (i.e. EUR interest rate yield curves and volatilities),

extreme aggregations onto a few (1-3) risk factors (pillar, pillar/strike) is often

sufficient to pass the test.

Principal component analysis is helpful to understand the most important risk factors

and to select the possible aggregations to be tested.

As a consequence, it seems that AVA MPU can be drastically reduced.

NEW


4: AVA calculationAVA Close-Out Costs (CoCo) [1]

AVA definitionAVA Close-Out Costs (CoCo) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in the exit price of the valuation positions, or, in other terms, the cost of liquidity that a particular valuation exposure can exhibit in particular market conditions. Both situations lead to relevant bid-ask spreads to exit the valuation position. Since illiquidity can also be seen as uncertainty around the mid price, AVA CoCooverlaps with AVA MPU. Thus, when AVA MPU is based on tradable prices, AVA CoCo may be set to zero.

AVA main referenceso EBA RTS, article 10. o EBA FAQs 23, 24, 24.1, 28, 30, 31, 37, 37.1, 40.1, 40.3, 42.5.

AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoCo refers in particular to those valuation positions for which there is not sufficient liquidity to exit the valuation exposure at mid price (at 90% confidence level), and there are relevant bid-ask spread.



AVA Fair Value The FV of the trades subject to AVA CoCo may include or not the effect of possible bid-ask spread. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover the most relevant bid-ask uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include such FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA CoCo (keeping the AVA non-negative).



Did you calculate 𝐴𝑉𝐴𝑀𝑃𝑈 for the same valuation exposure

based on exit prices ?

o Did you compute the mark to market on the assumption to

close out at mid market (see CRR art. 105.5) ?

o Is there evidence that sufficient liquidity exists to exit the

valuation exposure at mid-price at 90% confidence level ?

NO

Compute individual 𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 for each valuation exposure 𝑝𝑖to each bid-offer spread Δ𝑗 for each valuation input 𝑢𝑗

YES

YES

AVA Close Out Cost (CoCo) (EBA RTS, article 10) refers to the valuation uncertainty of a

valuation exposure arising from uncertainty in the exit price of the valuation positions.

NO

Continue

𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 = 0

Does the valuation position have a valuation exposure

𝑝𝑖 , 𝑖 = 1, … ,𝑁𝑝, to uncertainty of exit price ?

NO

YES



o Use the data sources defined in Art. 3.

o For non-derivative valuation positions, or derivative positions which are marked to market,

either refer to the instrument price, or decompose into each valuation input required to

calculate the exit price, treated separately.

o If a valuation input 𝑢𝑗 consists of a matrix of parameters, calculate AVA based on the

valuation exposures related to each matrix element.

o If a valuation input 𝑢𝑗 does not refer to tradable instruments, map the valuation input and

the related valuation exposure to a set of market tradable instruments.

Reduce the number of

parameters of the valuation

input for the purpose of

calculating AVAs ?

Continue

NO

P&L

variance

test

Positive

YES

Negative

Subject to independent

control function review

and internal validation on

at least an annual basis



Estimate a point Δ𝑗within the range with

90% confidence that

the bid-ask spread

that could be achieved

in exiting the valuation

exposure would be at

that price or better.

Use expert-based

approach using

qualitative and

quantitative information

available to achieve a

level of certainty in the

prudent valueΔ𝑗 that is

equivalent to 90%.

Do sufficient data exists to

construct a range of plausible bid-

offer spreads Δ𝑗 for a valuation

input 𝑢𝑗?

YES

NO

Notify competent

authorities of the

valuation exposures for

which this approach is

applied, and the

methodology used to

determine the AVA.

Continue



Compute individual APVA CoCo

𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝑤𝐶𝑜𝐶𝑜 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 − 𝑃𝑉𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗

Apply half of the bid-offer spread Δ𝑗to valuation exposure 𝑝𝑖 and compute prudent value

Compute total category level AVA CoCo

𝐴𝑉𝐴𝐶𝑜𝐶𝑜 𝑡 =

𝑖=1

𝑁𝑝

𝑗=1

𝑁𝑢

𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗

By exposure:

𝑃𝑉𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 −1

2

𝜕𝐹𝑉

𝜕𝑢𝑗Δ𝑗

By revaluation:

𝑃𝑉𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 ±1

2Δ𝑗 ,

or (when the uncertain input is the

instrument price):

𝑃𝑉𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖 , 𝑢𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑢𝑗 − 0.5 × Δ𝑗


AVA calculation

o Securities

• Securities held in market making portfolios

𝐴𝑉𝐴𝐶𝑜𝐶𝑜 𝑡 = 0, since, in these cases, the Institution makes both the bid and

the ask prices.

• Liquid securities accounted at Fair Value Level 1

a possible approach is

A𝑉𝐴𝐶𝑜𝐶𝑜 𝑡 = 𝑤𝐶𝑜𝐶𝑜𝐹𝑉(𝑡) ൝−ത𝑉𝑏𝑖𝑑 𝑡 long positions,

+ത𝑉𝑎𝑠𝑘 𝑡 short positions.

where ത𝑉𝑏𝑖𝑑(𝑡)/ ത𝑉𝑎𝑠𝑘 𝑡 are the average bid/ask prices quoted at time t, and

𝑤𝐶𝑜𝐶𝑜 = 0.5.

• Any other security

𝐴𝑉𝐴𝐶𝑜𝐶𝑜 𝑡 = 0 if, according to the Institution Fair Value Policy, they are

already priced at prudent bid or ask,

otherwise AVA CoCo shall be computed via sensitivity or full revaluation

based on relevant risk factors, in particular credit spread and interest rate

curves, using prudent bid-ask spread.



AVA calculation (cont’d)

o Derivatives

AVA CoCo is computed via sensitivity or full revaluation based on relevant risk

factors and on market price uncertainty in the bid-offer spread.

Exchange Traded Derivatives (ETD)

A𝑉𝐴𝐶𝑜𝐶𝑜 𝑡 = 0, since the FV is quoted and actively traded on the exchange

with negligible bid-ask, otherwise go to next case.

OTC Derivatives (OTCD)

AVA CoCo may be computed typically via full revaluation or sensitivity based

on relevant risk factors, similarly to AVA MPU.

Bid-ask MPU estimation

AVA CoCo calculation is based on the estimation of bid-ask MPUs of relevant risk

factors. Possible sources of such MPUs are restricted to those cases where the

market quotes multiple sources of bid-ask spread.

Examples

o Bond for which there exist multiple bid-ask contributors.



Case study of AVACoCo calculation for a security.

Top left: longpositions, ranking and percentiles of mid-bid differences, AVA CoCo = 0.71.

Top right: shortpositions, ranking and percentiles of ask-mid differences, AVA CoCo = 0.71.



AVA definitionAVA Model Risk (MoRi) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in models and model calibrations used by market participants. In particular, AVA MoRi does not refers to the uncertainty in market risk capital arising from model risk (see FAQ 23.1).

AVA main referenceso EBA RTS, article 11. o EBA FAQs 10, 23.1, 28.

AVA scope of applicationWithin the general prudent valuation scope (see before), AVA MoRi refers in particular to those valuation positions for which the Institution estimates that there is a lack of firm exit price due to model and/or model calibration choices. Of course, instruments which can be replicated by exact static combination of mark-to-market instruments should not contribute to AVA MoRi.

4: AVA calculationAVA Model Risk (MoRi) [1]


AVA Fair Value The FV of the trades subject to AVA MoRi may include or not the effect of possible model risk. In some particular cases, Institutions may account FV reserves in their balance sheets to cover the most relevant model risk uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include these reserves, or, in other words, the reserves must be subtracted from the AVA MoRi (keeping the AVA non-negative).



Does the valuation position 𝑝𝑖 , 𝑖 = 1,… , 𝑁𝑝, valued with

model 𝑀𝑗 , 𝑗 = 1,… ,𝑁𝑀, lacks of a firm exit price ?

YES

AVA Model Risk (MoRi) (EBA RTS, article 11) refers to the valuation uncertainty of a valuation

exposure arising from uncertainty in model usage and calibrations used by market participants.

Continue


NO

Is the valuation position 𝑝𝑖, valued with model 𝑀𝑗, sensitive

to the usage of different valuation models or model

calibrations 𝑀1, … ,𝑀𝑁𝑀 used by market participants ?

𝐴𝑃𝑉𝐴𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗 = 0

YES

Compute individual 𝐴𝑃𝑉𝐴𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗 for each

applicable valuation model 𝑀1, … ,𝑀𝑁𝑀

Does the valuation model risk arise from

calibrations from market derived parameters ?

NO

NO

YES

To be included

into 𝐴𝑉𝐴𝑀𝑃𝑈

Notation: the model scenarios 𝑀1, … ,𝑀𝑁𝑀 includes all the

possible models and calibrations appropriate to revaluate all

the valuation positions

Notation: typically, for a

given valuation exposure

𝑝𝑖, a single valuation

model 𝑀𝑗 is used



Estimate a point 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑀𝑗 within the

range with 90%

confidence to exit the

valuation exposure at

that price or better.

Use expert-based approach to estimate a

prudent value 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑀𝑗 considering:

o complexity of products relevant to the

model;

o diversity of possible mathematical

approaches and model parameters,

not related to market variables;

o one way market for relevant products;

o existence of unhedgeable risks in

relevant products;

o model adequacy to capture the

behavior of the pay-off of the products

in the portfolio.

Is it possible to construct a range of plausible valuations

produced from model scenarios 𝑀1, … ,𝑀𝑁𝑀 ?

YES

NO

Notify competent

authorities of the

models for which

this approach is

applied, and the

methodology used

to determine the

AVA.

Model risk test

Continue



Compute individual APVA MoRi

𝐴𝑃𝑉𝐴𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗 = 𝑤𝑀𝑜𝑅𝑖 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑀𝑗 − 𝑃𝑉𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗

Compute total category level AVA MoRi

𝐴𝑉𝐴𝑀𝑜𝑅𝑖 𝑡 =

𝑖=1

𝑁𝑝

𝑗=1

𝑁𝑀

𝐴𝑃𝑉𝐴𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗

Compute individual prudent value MoRi

𝑃𝑉𝑀𝑜𝑅𝑖 𝑡, 𝑝𝑖 , 𝑀𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑀𝑗

Notation: 𝐹𝑉 𝑡, 𝑝𝑖 , 𝑀𝑗 denotes

the prudent value of the valuation

exposure 𝑝𝑖 evaluated with model

𝑀𝑗 determined as above



Find a material sample of valuation models ෩𝑀 ⊂ 𝑀1, … ,𝑀𝑁 for which

AVA MoRi is computable via range of plausible values (art. 11.3)

Model risk test

For each valuation position subject to AVA MoRi

computed via expert-based approach (EBA RTS art. 11.4)

Compute AVA MoRi using expert based

approach (art. 11.4) applied to the

sample of models ෩𝑀

Compute AVA MoRi using a range of

plausible values (art. 11.3)

applied to the sample of models ෩𝑀

Compare the results and check the prudence of the expert-based

approach with annual frequency


AVA calculation

o Securities

• Securitizations

AVA MoRi may be calculated by stressing cash flows w.r.t. constant default rate

(CDR) and constant prepayment rate (CPR).

• CDOs

AVA MoRi my be calculated by stressing correlations, recoveries and weighted

average life (WAL).

• Impaired/defaulted securities

AVA MoRi is calculated by stressing the recovery rate.

o Derivatives

AVA MoRi may be computed using alternative models and/or model calibrations

applied to the corresponding valuation exposures.



Alternative models and calibrationsAVA MoRi is not based on any possible alternative model or model calibration, but on those specific alternative models or model calibrations that may reasonably used by market participants to price the same or similar valuation exposures.

Examples

o alternative but reasonable models, • calibrated to the same calibration basket

• Referred to the same group of financial instruments

o Same model, alternative calibration approaches, e.g. • different calibration baskets

• different calibration weights (e.g. flat, or vega weighted)

• different objective functions

• different optimization algorithm (e.g. global vs local)

• Etc.

o Same model, same calibration, alternative numerical approaches, e.g. • analitycal approximations

• semi-analitycal approximations

• numerical PDE solution

• Monte Carlo simulation

• etc.


Inspiration: «There’s

plenty of room at the

bottom»Richard Feynman, 1959

www.its.caltech.edu/~feynm

an/plenty.html


Market Risk Scenarios vs Model Risk Scenarioso Risk measures are typically linked to scenarioso Scenarios are related to the risk factors relevant for a particular risk typology


Risk class Scenarios Risk measures

Market risk Present market data VaR, Expected shortfall, etc.

Counterparty risk Future market data EPE, Effective EPE, etc.

Operational risk Operational loss event frequency

and severity

VaR 99.9%

Model risk Model scenarios

o Alternative models

o Alternative numerical approaches

o Alternative calibrations

K-th percentile of distribution

of model prices (10°

percentile for Prudent

Valuation)


Processes and controls relevant to model risk (EBA RTS art. 19.2, 19.3)o Annual review of model performanceo Independence in the validation process between risk taking and control units,o Institution-wide product inventory ensuring that every valuation position is

uniquely mapped to a product definitiono Defined valuation methodologies for each product of the inventory, including

calibration and measurement of the valuation uncertainty.o Validation process ensuring that for each product, the product level

methodologies are approvedo Defined thresholds based on observed market data for determining when

valuation models are no longer sufficiently robusto A new product approval process referencing the product inventory




Relationships between AVA MoRi and AVA MPU, AVA CoCo, fair value, fair value adj.

AVA = 0.5xMPU + 0.5xCoCo + 0.5xMoRi

Fair value

(mean)

Fair value

adjusted

MPU

adj.

Fair value adj.MoRi

AVA MoRi

CoCo

adj.

AVA CoCo

AVA MPU

MoRi

adj.



Historical sources of model riskPeriod Main driver Main risk factor Effects1987 Black Monday Volatility Volatility smile

2004 CMS market VolatilitySwaption volatility smile and CMS convexity adjustment

2004 IAS39 Credit Credit Risk Adjustment (CRA)2007 Credit crunch Credit, liquidity Subprime writedown2007 Credit crunch Interest rate basis Multiple yield curves

2009-2010 Credit crunch Interest rate basis CSA discounting2009-2010 Credit crunch Bilateral credit CVA & DVA (IFRS13, 2013)2013-2015 Credit crunch Funding Funding Valuation Adjustment (FVA)

2013-2014 Credit crunch Interest rateNegative interest rates and inflation, negative Floor strikes, Bond floater coupons floored, end of Black’s model.

2014- Credit crunch Capital charges Capital Valuation Adjustment (KVA)2017 Credit crunch Funding Bilateral initial margins


Market Risk Scenarios vs Model Risk Scenarioso Risk measures are typically linked to scenarioso Scenarios are related to the risk factors relevant for a particular risk typology

3: AVA calculationAVA MoRi: model risk scenarios vs traditional scenarios

Risk class Scenarios Risk measures

Market risk Present market data VaR, Expected shortfall, etc.

Counterparty risk Future market data EPE, Effective EPE, etc.

Operational risk Operational loss event frequency

and severity

VaR 99.9%

Model risk Model scenarios

o Alternative models

o Alternative numerical approaches

o Alternative calibrations

K-th percentile of distribution

of model prices (10°

percentile for Prudent

Valuation)


3: AVA calculationAVA MoRi: model risk scenarios for interest rate derivatives


3: AVA calculationAVA MoRi: model risk scenarios nested simulation

Pricing

model

OnePricing

model

Two

Pricing

model

Three

Idea of model risk in nested Monte Carlo Simulations for XVAso Scenarios are related to the risk factors relevant for a particular risk typologyo Primary scenarios are tranched into different groups, associated to different

simulation dynamicso At each future time simulation date, we use different pricing models, each

consistent with its underlying risk factors dinamics.

NEW


4: AVA calculationAVA Model Risk (MoRi): case study 1 [1]

Case study 1: model risk in interest rate yield curve construction

Interest rate yield curves are used everywhere for discounting and for interest rate derivatives and securities with floating rate coupons. So, this is an important case study.

Yield curve construction is based on recursive application of pricing formulas applied to interest rate market instruments. So, there is a lot of modelling inside.

In particular, the interpolation algorithm is very important, both pre and post bootstrapping:

o Simple but non-smooth linear interpolation algorithms are very simple and robust, but produces irregular forward curves

o Standard spline interpolation is less simple but produces oscillating yield curves

o Monotonic cubic spline interpolation is regular.



Linear interpolation on zero interest rates

Monotonic cubic spline interpolation on zero interest rates



Differences in bps between three different interpolation algorithms (linear, natural cubic spline and monotonic cubic spline) for a portfolio of 3 standard IRS on Euribor 1M, 6M, 12M + 3 standard Basis Swaps.



Case study 2: model risk experiment with Numerix

Sensitivity of prices to modelso Various dimensions of modelling decisionso Example of Bermudan swaption pricing with HW1F, HW2F, CIR, and BK modelso Impact of calibration choiceso AVA MoRi for a Bermudan swaptiono Model implied European swaption smile

Impact of changing market environment on model performanceo Handling of negative rateso Example of floor pricing with very low strikes by using various models

Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, available at www.numerix.com



Case study 2: model risk experiment with Numerix (cont’d) Global modelling approach

Trade

FX spotBasis

spreadYield Curve Correlation

Model

underlying

Forward

curveSwap rate

Risk factor

Short-rate

Distribution

typeNormalLog-normal Mixture

Chi-

squared

Model type HW1F HW2F

Calibration

instruments Caplets Swaptions

Instruments

configuration

10Y

diagonal

20Y

diagonal10Y column

10Y diag +

10Y column

CIR BK

CMS

…

…

…

…

…

…



Case study 2: model risk experiment with Numerix (cont’d)

Experiment

#Instruments Models Calibrations

Bermudan

swaption

• Coterminal bermudan payer

swaption

• Euribor 6M

• 10Y maturity

• Annual callability

• Sstrike ATM 10Y swap

• OIS discounting

• Hull-White 1 Factor

(HW1F)

• Black-Karasinski (BK)

• Cox-Ingersoll-Ross 1

Factor (CIR1F)

• Hull-White 2 Factors

(HW2F)

• Cox-Ingersoll-Ross 2

Factors (CIR2F)

• Set 1: 10 Y diagonal

swaption ATM

• Set 2: 10Y diagonal

and 1Y column

swaption ATM

• Set 3: 20Y diagonal

and 1Y column

swaption ATM

Caps/Floors

with negative

rates

• 5Y Floor

• Euribor 6M

• Negative and positive strikes

• Yield curves with negative

rates

• Linear interpolation and flat

extrapolation

• SABR interpolation and flat

extrapolation

• Black (analytic)

• Hull-White 1 Factor

(HW1F)

• Shifted Black-Karasinski

(SBK)

• Set 1: Cap volatility

columns for strikes

ATM and 1%

• Set 2: full Cap volatility

surface, with strikes

from 1% to 10%

Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, www.numerix.com



Overview of results

Prices range from 1.45% to 3.91% Normal models produce consistently higher PVs for all calibration sets compared to

non-normal models

HW1FBK

CIR1FHW2F

CIR2F

0.00%

1.00%

2.00%

3.00%

4.00%

Set1

Set2

Set3

Bermudan swaption prices per model and calibration set



Results by calibration set

Calibration set 1 (10Y diagonal) produces highest distribution of prices Average price is fairly stable across different calibration sets Same model stays consistently below or above the average price for all calibration

sets

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

Set1 Set2 Set3

Bermudan swaption prices per calibration set

HW1F BK CIR1F HW2F CIR2F Average



Results by model

HW1F and BK models exhibit lowest variations in prices with changing calibration set Prices of 1F and 2F models of the same model type can differ significantly

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

HW1F BK CIR1F HW2F CIR2F

Bermudan swaption prices per model

Set1 Set2 Set3



Results

Notional is 10m EUR Assuming Fair Value is the average of all price

Long swaption:o Fair Value: FV = 258k EURo Prudent value is the 10% percentile of all prices: PV = 177k EURo AVA MoRi = 0.5x(FV-PV) = 40.5k EUR

Short swaption:o Fair Value: FV = -258k EURo Prudent value is the 90% percentile of all prices: PV = -317k EURo AVA MoRi = 0.5x(FV-PV) = 29.5k EUR



Excluding models

All models All except HW2F All models All except HW2F

Fair Value (1) 258 258 -258 -258

Prudent Value 177 158 -317 -315

Model Risk AVA 40.5 50 29.5 28.5

Long swaption Short swaption

Fair Value (1) is computed as the average of all model prices

Fair Value (2) for “All except HW2F” is computed excluding the price of the HW2F model

All models All except HW2F All models All except HW2F

Fair Value (2) 258 240 -258 -240

Prudent Value 177 158 -317 -315

Model Risk AVA 40.5 41 29.5 37.5

Short swaptionLong swaption



Exercise probabilities

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23

Call probabilities per couponCalibration set 1

HW1F

BK

CIR

HW2F

CIR2F

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%



HW1F

BK

CIR

HW2F

CIR2F

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%



HW1F

BK

CIR

HW2F

CIR2F

Exercise probability per coupon CIR-type models imply a higher

probability of early exercise than HW models

The term structure of exercise probabilities is regular for all models for calibration set 1, humped for calibration sets 2 and 3.


AVA definitionAVA Unearned Credit Spread (UCS) refers to the valuation uncertainty in the credit valuation adjustment (CVA) to include, according to the applicable accounting framework, the current value of expected losses due to counterparty default on derivative positions. Such valuation uncertainty refers, in particular, to MPU, CoCoand MoRi uncertainties in the calculation of CVA. Hence, the RTS specifies that the AVA UCS shall be split into such components, to be aggregated to their corresponding AVA.Since the definition of AVA UCS specifies “losses due to counterparty default” (not “profits due to own default”), and the CRR, art. 33 states that the debt valuation adjustment (DVA, the gain on liabilities due to own credit quality) should not be included in the calculation of own funds, then AVA UCS shall not include the DVA component.

AVA main referenceso EBA RTS, article 12. o EBA FAQs 10, 25, 28.

4: AVA calculationAVA Unearned Credit Spread (UCS) [1]


AVA scope of applicationWithin the general prudent valuation scope (see before), AVA UCS refers in particular to those valuation positions subject to a credit valuation adjustment, and specifically, to OTC derivatives, with a particular focus on uncollateralized derivatives. Securities are excluded, since credit risk is already included in the security credit spread.

AVA Fair Value The FV of the trades subject to AVA UCS may include full, partial or null CVA. In any case the FV subject to prudent valuation for AVA UCS must include these CVAs.




AVA Unearned Credit Spread (UCS) (EBA RTS, article 12) refers to the valuation uncertainty in

the credit valuation adjustment to include, according to the applicable accounting framework, the

current value of expected losses due to counterparty default on derivative positions.

o Is the valuation position 𝑝𝑖 , 𝑖 = 1,… , 𝑁𝑝, a derivative position, and

o according to the applicable accounting framework, is an

adjustment necessary to include the current value of expected

losses due to counterparty default (CVA) ?

YES

NO

𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 = 0

Aggregate

𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝑀𝑃𝑈to APVA MPU.

Go to AVA MPU and apply

those rules to compute

individual AVA UCS w.r.t.

MPU, 𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝑀𝑃𝑈

Aggregate

𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝐶𝑜𝐶𝑜to APVA CoCo.

Go to AVA CoCo and apply



CoCo, 𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝐶𝑜𝐶𝑜

Aggregate

𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝑀𝑜𝑅𝑖to APVA MoRi.

Go to AVA MoRi and apply



MoRi, 𝐴𝑃𝑉𝐴𝑈𝐶𝑆 𝑡, 𝑝𝑖 , 𝑀𝑜𝑅𝑖


AVA calculation

o Securities: excluded

o Derivatives

• DVA component

𝐴𝑉𝐴𝑈𝐶𝑆 𝑡 = 0, since DVA is excluded from the prudent valuation scope.

• CVA component

𝐴𝑉𝐴𝑈𝐶𝑆 𝑡 shall be calculated considering the following components.

Unilateral CVA: since DVA is excluded, Institutions shall consider the

unilateral CVA, without first to default conditioning.

𝐴𝑉𝐴𝑈𝐶𝑆 𝑡,𝑀𝑃𝑈 : uncertainty in CDS spreads, PDs and recovery rates,

uncertainty in risk factors used to compute the exposure (e.g. curves,

volatilities)

𝐴𝑉𝐴𝑈𝐶𝑆 𝑡, 𝐶𝑜𝐶𝑜 : bid/ask in CDS spreads.

𝐴𝑉𝐴𝑈𝐶𝑆 𝑡,𝑀𝑜𝑅𝑖 : unilateral vs bilateral CVA, time simulation grid, risk free vs

risky close-out, wrong way risk, different dynamics to simulate underlying risk

factors and compute the exposure.

• No CVA case

if the CVA is not included in the accounting fair value for some valuation

positions, 𝐴𝑉𝐴𝐶𝑉𝐴 𝑡 shall be equal to the full CVA of those position, calculated

using prudent parameters as above.



AVA definitionAVA Investing and Funding Costs (IFC) refers to the valuation uncertainty in the funding costs used when assessing the exit price of a valuation position, according to the applicable accounting framework. Such valuation uncertainty refers, in particular, to MPU, CoCo and MoRiuncertainties in the calculation of the funding cost. Hence, AVA IFC shall be split into such components, to be aggregated to their corresponding AVAs.


AVA scope of applicationWithin the general prudent valuation scope (see before), AVA IFC refers in particular to those valuation positions subject to a funding valuation adjustment and specifically, to OTC derivatives. Securities are excluded, since funding risk is already included in the security credit spread

AVA Fair Value The FV of the trades subject to AVA IFC may include full, partial or null FVA. In any case the FV subject to prudent valuation for AVA IFC must include these FVAs.

4: AVA calculationAVA Investing and Funding Costs (IFC) [1]



AVA Investing and Funding Cost (IFC) (EBA RTS, article 13)

refers to the valuation uncertainty in the funding costs used when assessing the exit price

according to the applicable accounting framework

o Is the valuation position 𝑝𝑖 , 𝑖 = 1,… ,𝑁𝑝, a derivative position, and

o according to the applicable accounting framework, is an

adjustment necessary to include the funding costs in the exit

price (FVA) ?

YES

NO 𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 = 0

Aggregate

𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝑀𝑃𝑈to APVA MPU.

Go to AVA MPU and apply


individual AVA IFC w.r.t.

MPU, 𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝑀𝑃𝑈

Aggregate

𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝐶𝑜𝐶𝑜to APVA CoCo.

Go to AVA CoCo and apply



CoCo, 𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝐶𝑜𝐶𝑜

Aggregate

𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝑀𝑜𝑅𝑖to APVA MoRi.

Go to AVA MoRi and apply



MoRi, 𝐴𝑃𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑝𝑖 , 𝑀𝑜𝑅𝑖


AVA calculation

o Securities: excluded

o Derivatives

• Strongly collateralized derivatives

𝐴𝑉𝐴𝐹𝑉𝐴 𝑡 = 0 if the funding cost is already included in the FV using OIS

discounting methodology.

• Non-Strongly collateralized derivatives

If the FVA is included in the accounting FV for some valuation positions, AVA

IFC shall be calculated as the FVA uncertainty, resulting from the uncertainty

in the funding curve.

If the FVA is not included in the accounting FV for some valuation positions,

𝐴𝑉𝐴𝐹𝑉𝐴 𝑡 shall be equal to the full FVA of those position, calculated using

prudent parameters.

• CSA with initial margins

AVA IFC shall computed on the initial margins, using a discounting approach

applied to an exposure profile assigned to the future initial margin.




• 𝐴𝑉𝐴𝐼𝐹𝐶 𝑡 shall be calculated considering the following components.

𝐴𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑀𝑃𝑈 : uncertainty in funding spreads, PDs and recovery rates,

uncertainty in risk factors used to compute the exposure (e.g. curves,

volatilities)

𝐴𝑉𝐴𝐼𝐹𝐶 𝑡, 𝐶𝑜𝐶𝑜 : bid/ask in funding spreads.

𝐴𝑉𝐴𝐼𝐹𝐶 𝑡, 𝑀𝑜𝑅𝑖 : time simulation grid, different dynamics to simulate

underlying risk factors and compute the exposure.

Funding spread estimationAVA IFC calculation is based on the estimation of a prudent funding curve. Possible sources of such yield curve is the bond yield curve based on own Institution bond emissions.



Switch to FVA accounting

“[JPM] implemented a FVA framework this quarter for its OTC derivatives and structured notes, reflecting an industry migration towards incorporating the cost or benefit of unsecured funding into valuations. For the first time this quarter, we were able to clearly observe the existence of funding costs in market clearing levels. As a result, the firm recorded a $1.5 billion loss this quarter.” (source: M. Cameron, Risk Magazine, 14 Jan. 2014)

Bank 2012 2013

Barclays -£101 MM ?

Deutsche Bank -- -€364 MM

Goldman Sachs ? ?

JP Morgan -- -$1.500 MM

Lloyds Banking Group - £143 MM -£135 MM

Nomura -- -¥10.000 MM (-$98 MM)

Royal Bank of Scotland - £475 MM -£424 MM

Societè Generale ? ?

UBS -- --


AVA definitionAVA Concentrated Positions (CoPo) refers to the valuation uncertainty in the exit price of concentrated positions.Such valuation uncertainty refers, in particular, to those valuation positions showing concentrated exposures related to:o the size relative to the liquidity of the related market;o the average daily market volume and typical daily trading volume of the institution;o the institution’s ability to trade in that market, and to exit the valuation position

within the time horizon implied by the market risk capitalization (10 days) without impacting the market.


AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to concentration risk as defined above.

AVA Fair Value The FV of the trades subject to AVA CoPo typically does not include a CoPocomponent.

3: AVA calculationAVA Concentrated Positions (CoPo) [1]



AVA Concentrated Positions (CoPo) (EBA RTS, article 14)

refers to the valuation uncertainty in the exit price of concentrated positions

Identify concentrated valuation positions 𝑝𝑖 , 𝑖 = 1,… ,𝑁𝑝, considering:

o the size of all valuation positions relative to the liquidity of their related market,

o the institution’s ability to trade in that market,

o the average daily market volume and typical daily trading volume of the institution.

YES

NO

𝐴𝑃𝑉𝐴𝐶𝑜𝑃𝑜 𝑡, 𝑝𝑖 = 0

For each concentrated valuation position 𝑝𝑖, there exists

a market price applicable for the size of the position ?

Estimate a prudent exit period

Does the prudent exit period exceed 10 days ?

Continue

YES

NO



Compute individual AVA CoPo taking into

account:

o the volatility of the valuation input,

o the volatility of the bid offer spread,

o the impact of the hypothetical exit

strategy on market prices.

Document the methodology

applied to determine

concentrated valuation positions

for which a concentrated

positions AVA is calculated

Compute total category level AVA CoPo

𝐴𝑉𝐴𝐶𝑜𝑃𝑜 𝑡 =

𝑖=1

𝑁𝑝

𝐴𝑃𝑉𝐴𝐶𝑜𝑃𝑜 𝑡, 𝑝𝑖


AVA calculation

o Securities

AVA CoPo may be calculated as follows:

• Look for possible concentrated positions by comparing the size held w.r.t. the

outstanding amount of the security circulating on the market,

• estimate coefficients of uncertainty related to the sizes above,

• compute AVA CoPo via sensitivity on the credit risk factors and uncertainties

above.

o Derivatives

OTC derivatives typically do not show concentrated positions in the sense defined

above. Possible exceptions shall be documented and AVA CoPo shall be

calculated as described in the previous scheme.

Exampleso Concentrated positions into single stock w.r.t. typical stock trading volumeso Concentrated positions into single bond emissions w.r.t. typical bond trading

volumes and outstanding amount.


w.r.t. typical stock trading volumes


AVA definitionAVA FAC takes into account the valuation uncertainty emerging from possible administrative costs and future hedging costs on valuation positions for which a direct exit price is not applied for the close-out costs AVA. Thus, future administrative costs are complementary to close-out costs. If the close-out costs are assessed on a full exit price basis then, after executing the corresponding close out strategy, the positions disappear, and there are no future administrative costs. However, where close-out costs are assessed on a "cost-to hedge" basis, as with derivative portfolios, the positions are maintained, and therefore there are possible future administrative costs in running the portfolio until maturity.

AVA main referenceso EBA RTS, article 15. o EBA FAQs 37, 37.1.

AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to FAC as defined above.

4: AVA calculationAVA Future Administrative Costs (FAC) [1]


AVA Fair Value The FV of the valuation positions typically does not include the effect of possible future administrative costs, since such costs are specific of each institution and do not regard an exit price according to IFRS. Hence, the AVA FAC must be applied directly to the full FV of valuation positions.




AVA Future Administrative Costs (FAC) (EBA RTS, article 15)

refers to the valuation uncertainty due to future administrative and hedging costs

YES 𝐴𝑃𝑉𝐴𝐹𝐴𝐶 𝑡, 𝑝𝑖 = 0Do you calculate 𝐴𝑃𝑉𝐴𝑀𝑃𝑈 and 𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 for a valuation

exposure 𝑝𝑖 , 𝑖 = 1,… ,𝑁𝑝,, which imply fully exiting the exposure ?

Compute individual APVA FAC taking into account:

o administrative costs, including all incremental staffing and fixed costs that will be incurred in

managing the portfolio, over the expected life of the valuation exposures,

o the future hedging costs over the expected life of the valuation exposures,

o the cost reduction as long as the size of the valuation exposure reduces,

o the term structure of discounts at risk free rate.

NO

Compute total category level AVA FAC

𝐴𝑉𝐴𝐹𝐴𝐶 𝑡 =

𝑖=1

𝑁𝑝

𝐴𝑃𝑉𝐴𝐹𝐴𝐶 𝑡, 𝑝𝑖



AVA calculationConsidering the regulatory requirements, we may write a general formula for AVA FAC

𝐴𝑃𝑉𝐴𝐹𝐴𝐶 𝑡, 𝑝𝑖 = න𝑡

𝑇

𝑃 𝑡, 𝑢 𝐴𝑑𝐶 𝑡, 𝑢, 𝑝𝑖 𝑁𝐹𝐴𝐶 𝑡, 𝑢, 𝑝𝑖 𝑑𝑢

whereo 𝑃 𝑡, 𝑢 = discount factor over the time interval 𝑡, 𝑢 ,o 𝐴𝑑𝐶 𝑡, 𝑢, 𝑝𝑖 = administrative costs expected at time t for future time interval

𝑢, 𝑢 + 𝑑𝑢 , per unit of currency,o 𝑁𝐹𝐴𝐶 𝑡, 𝑢, , 𝑝𝑖 = nominal of the valuation exposure at future time u,o T = exipry date of the valuation exposure

Considering constant administrative costs and a decreasing step-wise constant notional struck on dates 𝑇1, … , 𝑇𝑀 , 𝑡 < 𝑇1, 𝑇𝑀 = 𝑇, we may write a discrete formula

𝐴𝑃𝑉𝐴𝐹𝐴𝐶 𝑡, 𝑝𝑖 ≅ 𝐴𝑑𝐶 𝑡, 𝑝𝑖

𝑘=𝑇1

𝑇𝑀

𝑃 𝑡, 𝑇𝑘 𝑁𝐹𝐴𝐶 𝑡, 𝑇𝑘 , 𝑝𝑖 𝑇𝑘 − 𝑇𝑘−1 .

Considering furthermore a single (weighted) average lifetime 𝑇𝑎𝑣𝑔 (WAL) we may

further simplify to

𝐴𝑃𝑉𝐴𝐹𝐴𝐶 𝑡, 𝑝𝑖 ≅ 𝐴𝑑𝐶 𝑡 𝑃 𝑡, 𝑇𝑎𝑣𝑔 𝑁𝐹𝐴𝐶 𝑡, 𝑇𝑎𝑣𝑔 𝑇𝑎𝑣𝑔 − 𝑡 .



AVA calculation (cont’d)Clearly, the administrative cost 𝐴𝑑𝐶 𝑡, 𝑝𝑖 is the most difficult data to obtain. We stress that in the formula above 𝐴𝑑𝐶 𝑡, 𝑝𝑖 refers to the cost per unit of time and currency, not to the total cost of the desk or the institution, which manage other portfolios not subject to AVA.

AVA dataAVA FAC calculations require the following input data.o Valuation positions not at full exit price, with nominal amounts and maturities.o Administrative and hedging costs per unit of time, per currency, per desk, per

activity.o Risk free (OIS) discount term structure until portfolio maturity.


AVA definitionAVA Early Termination (EaT) refers to the valuation uncertainty emerging from potential losses arising from non-contractual early terminations of client trades.

AVA main referenceso EBA RTS, article 16. o EBA FAQs 38.

AVA scope of applicationWithin the general prudent valuation scope (see before), AVA EaT regards in particular client trades, that is, trades with client counterparties that may be subject to non-contractual early termination because of litigations or commercial reasons.

AVA Fair Value The FV of the client trades subject to AVA EaT typically does not include the effect of possible non-contractual early terminations by clients. In some particular cases, Institutions may account reserves in their balance sheets to cover possible losses related to early terminations of some trades or portfolios with specific counterparties. If these reserves are accounted as a FV component, the FV subject to prudent valuation for AVA EaT must include the reserves. In other words, the reserves must be subtracted from the AVA EaT.

4: AVA calculationAVA Early Termination (EaT) [1]



AVA Early Termination (ET) (EBA RTS, article 16)

reflects the valuation uncertainty arising from potential losses

due to possible non-contractual early terminations of client trades.

YES

Is the valuation position 𝑝𝑖 , 𝑖 = 1,… ,𝑁𝑝,

subject to possible non-contractual early termination ?

Identify a suitable past time window 𝑇; 𝑡 and historical trades 𝑢𝑗 =

1,… , 𝑁𝐸𝑎𝑇 subject to non-contractual early terminations at past dates

𝑇𝑁𝐸𝑎𝑇 , … , 𝑇1 such that 𝑇 ≤ 𝑇𝑁𝐸𝑎𝑇 ≤ ⋯ ≤ 𝑇1 ≤ 𝑡.

NO

Retrieve the corresponding historical fair values 𝐹𝑉 𝑇𝑗 , 𝑢𝑗and actual termination prices 𝑃 𝑇𝑗 , 𝑢𝑗 .

Continue

𝐴𝑃𝑉𝐴𝐸𝑎𝑇 𝑡, 𝑝𝑖 = 0



The 10th percentile

may be negative (loss)

or positive (profit), and

represents the highest

loss or the smallest

profit realized with

90% historical

probability.

Compute individual APVA EaT according to the formula

𝐴𝑃𝑉𝐴𝐸𝑎𝑇 𝑡, 𝑝𝑖 = ቊ0, 𝑖𝑓 𝑃𝐿10% ≥ 0,

𝑃𝐿10% × 𝐹𝑉 𝑡, 𝑝𝑖 𝑖𝑓 𝑃𝐿10% < 0.

Calculate

o the historical profit and loss values, 𝑃𝐿 𝑇𝑗 , 𝑢𝑗 ∶= ൗ𝑃 𝑇𝑗 , 𝑢𝑗 − 𝐹𝑉 𝑇𝑗 , 𝑢𝑗 𝐹𝑉 𝑇𝑗 , 𝑢𝑗 ,

o the historical P&L distribution, ΤΔ𝑁 Δ𝑃𝐿 ,o the 10th percentile of the P&L distribution, 𝑃𝐿10% ≔ ℙ ΤΔ𝑁 Δ𝑃𝐿 , 10% ,

Compute total category level AVA EaT

𝐴𝑉𝐴𝐸𝑎𝑇 𝑡 =

𝑖=1

𝑁𝑝

𝐴𝑃𝑉𝐴𝐸𝑎𝑇 𝑡, 𝑝𝑖



AVA calculationSee flow chart above.

AVA dataAVA EaT calculations require a database of historical early terminations, including, for each trade:o termination date,o nominal,o fair value at EaT time instant,o actual EaT price at EaT time instant.

Exampleso Trades early terminated because of litigationso Trades early terminated because of commercial relationships



Case studySee figure below.



Case study (cont’d)o The nominal of the present portfolio of client trades subject to possible non-contractual EaT

(cols. 2-4 top, 12 €mln) is taken from “Derivatives HFT” in the sample portfolio. o The absolute FV is set to 5% of the nominal for 1,000 trades. o The past portfolio is set to half the present portfolio and may be seen as an average over the

EaT historical window (so, trading volume increased from past to present). o The portfolio of client trades that were historically early terminated (cols. 5-7 top) is set to 1%

of the past portfolio, hence the historical probability of non-contractual EaT is 1%. o In the bottom table we show a possible drill-down of the 10 trades historically affected by

non-contractual EaT. We generated the absolute EaT price (col. 4) as P=FV(1+10%ε), where ε is a random number with uniform distribution in [-1,1].

o Hence, the P&L (cols. 5-6) may be positive or negative (we chose a negative case). o Given the relative P&L% distribution (col. 6), we calculated the 10th percentile (which, in this

simple case with 10 trades, is just the 2nd higher P&L%), representing the highest loss happened with 90% historical probability after non-contractual EaT.

o Finally, we applied such historical estimate to the absolute FV of the present portfolio in the top table (col. 9-10).

o The AVA (col. 11) is just the absolute value of the corresponding expected loss (col. 9). o We notice that the historical P&L%(10) (-9.64%) corresponds to a small historical loss (-

28,917€) originated by a single deal with limited fair value (300.000€) but generates a much larger expected loss (-578,346€) once applied to the fair value of the present portfolio (6,000,000€). This is consistent with the idea of prudent value at 90% confidence level required by the regulation.


AVA definitionAVA Early Termination (EaT) takes into account the valuation uncertainty emerging from potential losses that an institution may incur because of the operational risk related to valuation processes. This risk is mainly related, but not limited, to the balance sheet substantiation process and to possible legal disputes (RTS art. 17.1). The main driver for AVA OpR is the operational risk framework adopted by the Institution. Institutions adopting the Advanced Measurement Approach (AMA) Operational Risk defined in the CRR, title III, ch. 4, art. 321-324 (AMA Institutions) are allowed a lighter AVA OpR, as described below. This facilitation is intended to avoid double counting of capital reserves related to the same source of risk. In all other cases (non-AMA Institutions), the AVA OpR is given by 10% of the sum of AVA MPU and AVA CoCo, which can result in high figures. In particular, FAQ 39, remarks that Institutions using the Standardized Method for Operational Risk defined in the CRR, title III, ch. 3, art. 317-320, cannot show that they already take into account the operational risk related to valuation processes. Thus they are not allowed to calculate AVA OpR as AMA institutions. .


4: AVA calculationAVA Operational Risk (OpR) [1]


AVA scope of applicationWithin the general prudent valuation scope (see before), AVA OpR regards in particular those positions that:o can be considered subject to operational risk during the valuation process;o for which in the balance sheet there are provisions for operational risk.Evidences of operational risk related to valuation process are the inclusion of those valuation processes as part of the AMA accounting for the mispricing, misselling and the process execution errors. Furthermore, an AMA usually accounts provision for legal disputes with clients where the underlying of the contract is a fair value position.

AVA Fair Value The fair values of positions under AVA OpR typically does not include any component or adjustment related to operational risk, since these factors do not concur to an exit price. From a risk management point of view, expected operational risk losses may be evaluated using scenario analysis and historical data related to realized operational risk losses.




AVA Early Termination (ET) (EBA RTS, article 17) reflects the

reflects the valuation uncertainty arising from potential losses

that may be incurred as a result of operational risk related to valuation processes.

Identify valuation positions 𝑝𝑖 , 𝑖 = 1, … ,𝑁𝑝, judged to be at-risk during the balance sheet

substantiation process, including those due to legal disputes.

Compute individual APVA OpR according to the formula

𝐴𝑃𝑉𝐴𝑂𝑝𝑅 𝑡, 𝑝𝑖 = 10% × 𝐴𝑃𝑉𝐴𝑀𝑃𝑈 𝑡, 𝑝𝑖 + 𝐴𝑃𝑉𝐴𝐶𝑜𝐶𝑜 𝑡, 𝑝𝑖

Is the AMA (Advanced Measurement Approach) applied to Operational Risk (as defined

in Title III Chapter 4 of Regulation (EU) No 575/2013) for valuation positions 𝑝𝑖 ?

Is there evidence that the operational risk relating to valuation processes of valuation positions 𝑝𝑖 is fully accounted for by the AMA calculation ?

YES

NO

𝐴𝑃𝑉𝐴𝑂𝑝𝑅 𝑡, 𝑝𝑖 = 0

NO

YES

Compute total category level AVA OpR

𝐴𝑉𝐴𝑂𝑝𝑅 𝑡 =𝑖=1

𝑁𝑝𝐴𝑃𝑉𝐴𝑂𝑝𝑅 𝑡, 𝑝𝑖


Summary

5. Prudent valuation frameworko Implementationo Methodological frameworko Operational frameworko IT frameworko Documentation & reportingo Example of prudent valuation framework


5: Prudent valuation framework Areas: overview

Governance Methodology

TechnologyDocumentation

and reporting

Institution


5: Prudent valuation framework Areas: governance

Define Prudent Valuation processes and controls

throughout the operative chain

Apply Indipendent Price Verification (IPV) processes

Guarantee effective controls to govern all fair valued

positions

Implement controls to ensure robust evaluation

processes even in stressed situations

Design reports for Senior Management (information,

frequency and recipients)

Deliver an exhaustive information set to guarantee

an appropriate understanding of the valuation

uncertainty of the assets and liabilities portfolio.

Implement the governance area in terms of roles, responsabilities and processes for

measurement, management and control.

Governance


5: Prudent valuation framework Areas: methodology

Design AVA calculation methodologies and

aggregation rules

Define scope at single legal entity level and

consolidated level

Design, realisation and maintenance of a prudent

valuation policy, subject to senior management

approval and revision.

Define robust methodologies to estimate and aggregate prudent values at banking group

level and consolidated level.

Methodology


5: Prudent valuation framework Areas: documentation and reporting

Production chain of prudent values (AVAs)

Match calculation schedule with regulatory deadlines

Deliver AVAs for internal and external reporting

Integrate prudent valuations (AVAs) calculation into the management and regulatory

reporting processes.

Documentation

and reporting


5: Prudent valuation framework Areas: technology

Integration with accounting repositories to determine

the prudent valuation scope

Implementation of feeds and calculation engine

Integration with regulatory reporting platform

Monitoring and control input/output data

Development management reporting tools

Design and implement an automatic IT chain for feeding and calculation processes of

prudent values

Technology


5: Prudent valuation framework Example of Prudent Valuation framework [1/4]

Scope Calculation Reporting

Identify fair value positions

Apply exlusionsprovided by the regulator:

o Positions subject to prudential filters such that fiar

value variations has no or partial impact on CET1

(es. AFS)

o Hedge Accounting positions

o Back to back positions

Monitor of output data quality

Data mining

Legal entities

scope

Prudent Valuation

scope

Prudent

valuation

scope

Accounting

systems



Identifiy uncertainty levels

Retrieval information from market operators

Retrieval Markit information

Data mining

Front

office

systems

External

sources

Uncertainty

levels




Check the threshold for core approach (EUR15 bn)

If > = EUR15 bn :

o Apply association rules between each single trade and

the corresponding AVAs

o Apply netting rules

o Aggregation and association of uncertainty levels with

single trades and AVAs

o Apply core AVA calculation rules

if < EUR15bn:

o 0,1% Prudent Valuation scope fair value

Data mining

Prudent Value

calculation

Prudent

valuation

scope

Uncertainty

levels

Methodology



Custom

reporting


Prepare management reporting

Prepare regulatory reporting (quarterly)

Transmit information to each stakeholder inside the bank

Data mining

Methodology

Management

reporting

Regulatory

reporting



6: ConclusionsHot topics (1/2)

The CRR is in place since 1st Jan. 2014, and EBA RTS are in the final phase ofapproval, so prudent valuation is mandatory.

AVA calculation for all fair value positions under the core approach is resourceintensive.

The practical application of the EBA RTS requires a lot of expert judgment, inparticular to achieve the required 90% level of certainty in the prudent value.

P&L variance test for AVA market price uncertainty and close out costs is ratherdifficult and controversial.

AVA Investing & Funding cost is a “prudent version” of the FVA, so banks still notaccounting FVA in their balance sheets should account the full FVA in the prudentvaluation, with the benefit of the diversification factor 0.5. Banks already accountingFVA must calculate a prudent FVA. .

Other XVAs, i.e. MVA (Margin Valuation Adjustment), and KVA (Capital ValuationAdjustment) are controversial. Rule of thumb could be “no fair value accounting, noprudent value capital”.


6: ConclusionsHot topics (2/2)

Unclear how to manage exclusions for back to back and hedge accounting positions.Is it referred to both Cash Flow Hedge (for which prudential filter is applied) and FairValue Hedge ?

AVAs have to be deducted from CET1. Hence, possible double counting w.r.t. othercapital deductions should be considered, e.g. expected loss amounts (CRR, art. 158-159), day one profits, etc.

Possible uneven playing field between institutions subject or not to the EU prudentvaluation rules.

New regulation and lack of standard market practices allows for widely differentapplications of the same rules across different institutions. It is reasonable to expectfollow ups from Regulators.


6: Conclusions

Questions & Answers


7: Selected ReferencesRegulations [1]

1) BCBS, “International Convergence of Capital Measurement and Capital Standards – A revised framework”, June 2004, http://www.bis.org/publ/bcbs107.htm

2) BCBS, “Revision of the Basel II market risk framework”, July 2009, http://www.bis.org/publ/bcbs158.htm

3) Financial Services Authority, “Dear CEO Letter: Valuation and Product Control”, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf

4) Financial Services Authority, “Product Control Findings and Prudent Valuation Presentation”, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf

5) Financial Services Authority, “Regulatory Prudent Valuation Return”, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml

6) International Accounting Standards Board, «International Financial Reporting Standards 13 –Fair Value Measurment», 1° Jan. 2013, www.ifrs.org

7) Regulation EU N.575/2013 of the European Parliament and of the Council on prudential

requirements for credit institutions and investment firms and amending Regulation EU

N.648/2012, 26 June 2013

8) European Banking Authority, “Discussion Paper relating to Draft Regulatory Technical

Standards on prudent valuation under Article 100 of the draft Capital Requirement Regulation (CRR)” EBA/DP/2012/03, 13 November 2012, http://www.eba.europa.eu/-/eba-

discussion-paper-on-draft-regulatory-standards-on-prudent-valuation.



9) European Banking Authority, “Consultation Paper Draft Regulatory Technical Standards on

prudent valuation under Article 105(34) of Regulation (EU) 575/2013 (Capital Requirements

Regulation – CRR)”, EBA/CP/2013/28, 10 July 2013, http://www.eba.europa.eu/regulation-and-policy/market-risk/draft-

regulatory-technical-standards-on-prudent-valuation.

10) European Banking Authority, “Questions and Answers on prudent valuation”, October 2013, http://www.eba.europa.eu/-/revised-faqs-on-prudent-valuation-q-1.

11) European Banking Authority, “Quantitative Impact Study on prudent valuation”, November 2013, http://www.eba.europa.eu/-/eba-launches-qis-exercise-on-prudent-

valuation.

12) Bank of Italy, Circolare 285, “Disposizioni di vigilanza per le banche”, 17 December 2013, https://www.bancaditalia.it/compiti/vigilanza/normativa/archivio-

norme/circolari/c285/index.html

13) European Banking Authority, “EBA final draft Regulatory Technical Standards Regulatory

Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013

(Capital Requirements Regulation – CRR)”, 31 March 2014, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft-

regulatory-technical-standards-on-prudent-valuation



14) European Banking Authority, “EBA final draft Regulatory Technical Standards Regulatory

Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013

(Capital Requirements Regulation – CRR)”, rev1, 23 January 2015, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft-

regulatory-technical-standards-on-prudent-valuation

15) European Commission, Commission delegated regulation (EU) 2016/101, supplementing

Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to

regulatory technical standards for prudent valuation under Article 105 (14), 26 Oct. 2015, http://ec.europa.eu/transparency/regdoc/rep/3/2015/EN/3-2015-7245-

EN-F1-1.PDF

16) European Banking Authority, Consultation Paper, “Draft Implementing Technical Standards

amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016, https://www.eba.europa.eu/-/eba-seeks-comments-

on-reporting-of-prudent-valuation-information

17) BCBS Consultative Document, “Pillar 3 disclosure requirements – consolidated and enhanced

framework”, March 2016, issued for comment by 10 June 2016, http://www.bis.org/bcbs/publ/d356.htm


7: Selected ReferencesPapers

1) Richard Roll, “A simple implicit measure of the effective bid-ask spread in an efficient

market”, The Journal of Finance, Vol. XXXIX, n. 4, Sept. 1984.

2) E. Derman, "Model Risk", Goldman Sachs Quantitative Strategies Research Notes, Apr.

1996.

3) R. Rebonato, "Theory and Practice of Model Risk Management”, Quantitative Research

Centre (QUARC) of the Royal Bank of Scotland, 2002.

4) R. Cont, "Model uncertainty and its impact on the pricing of derivative instruments",

Mathematical Finance, Vol. 16, No. 3, July 2006, 519–547.

5) R. Brar, “A Regulatory Perspective on Prudent Valuation and Best Practice in Product

Control”, in “Managing Illiquid Assets”, E. Takagawa editor, Risk Books, 2012.

6) Tanguy Dehapiot, “Prudent Value”, Risk Minds presentation, Dec. 2014.


7: Selected ReferencesOthers

1) Ernst & Young, “Prudent Valuation”, 24 May 2013.

2) Ernst & Young, “BIS III – Prudent Valuation – AVAs Overview and relations to IFRS13”,

July 2013.

3) Deloitte, “Prudent Valuation”, August 2013, http://www.deloitte.com/assets/Dcom-

Belgium/Local%20Assets/Documents/EN/Insights/FSI/be-fsi-

prudentvaluation_ebaconsultationpaper_aug2013.pdf.

4) Financial Machineries, http://www.financial-machineries.com.

5) AIFIRM, Associazione Italiana Financial Industry Risk Managers, “Prudent Valuation -Guidelines and sound practices“, Mar. 2016, http://www.aifirm.it/position-paper-prudent-valuation


10 Dec. 2014: Risk Minds Conference, joint talk on prudent valuation with T. Dehapiot.

28 May 2014: London Stock Exchange, Milano, prudent valuation course, M.

Bianchetti, U. Cherubini, E&Y.

16 May 2014: ABI conference, Roma, talk “Funding Valuation and Prudent Valuation

Adjustments (PVA & FVA)”, M. Bianchetti, U. Cherubini

24 Sept. 2014: corso ABI, Milano, talk “Prudent valuation“, M. Bianchetti, P. Virgili.

12 Nov. 2014: webinar Numerix, “Prudent Valuation: Bridging the Gap Between

Pricing & Risk Management”, M. Bianchetti (link).

24 Nov. 2014: London Stock Exchange, Milano, prudent valuation course, M.

Bianchetti, U. Cherubini, E&Y.

10 Dec. 2014: Risk Minds, Amsterdam, talk “Prudent Valuation - Bridging Pricing And

Risk Management”, M. Bianchetti (link).

25 Mar. 2015: WBS 4th CVA conference, London, corso “Prudent valuation“, M.

Bianchetti, U. Cherubini (link)

May 2015: Global Derivatives, Amsterdam, talk “Prudent Valuation - Bridging Pricing

And Risk Management”, M. Bianchetti (link).

7: Selected ReferencesEvents

http://nx.numerix.com/On-Demand-Webinar-Prudent-Valuation-Bridging-The-Gap-Between-Pricing-And-Risk-Management_Registration-Page.html

http://www.riskmindsinternational.com/

http://www.wbstraining.com/php/conferences/?id=33

http://www.icbi-derivatives.com/


APVA = Additional Prudent Valuation Adjustment AVA = Additional Valuation Adjustmento MPU = Market Price Uncertaintyo CoCo = Close out Costso MoRi = Model Risko UCS = Unearned Credit Spreado IFC = Investing and Funding Costso CoPo = Concentrated Positionso FAC = Future Administrative Costso EaT = Early Terminationo OpR = Operational Risks

CRR = Capital Regulatory Requirements EBA = European Banking Authority EU = European Union FV = Fair Value FVP = Fair Value Policy PV = Prudent Value PVA = Prudent Valuation Adjustment PVP = Prudent Value Policy QA = EBA Questions & Answers to DP and QIS RTS = EBA final draft Regulatory Technical Standards

8: Glossary


Disclaimer and acknowledgments

Disclaimer

The views and the opinions expressed here are those of the author and do not

represent the opinions of his employer. They are not responsible for any use that may

be made of these contents. No part of this presentation is intended to influence

investment decisions or promote any product or service.

Acknowledgments

The authors gratefully acknowledges

o E. Maffi, S. Vasconi, F. Bertolini, M. Benvenuti, A. Pignataro, S. Vella from E&Y for

their contribution to develop the prudent valuation framework and some data

analysis.

o I. Faerman from Numerix for his contribution for model risk examples.

o T. Dehapiot for sharing information and experties on the subject.

o Members of the AIFIRM committee on market risk for the stimulating discussions on

prudent valuation methodology and applications.

o Many other colleagues in Front Office and Risk Management of Intesa Sanpaolo for

creating a fertile environment to grow the seeds of prudent valuation.

Prudent Valuation

Economy & Finance

Transcript of Prudent Valuation