Trends in Economic Capital Modeling: Curt Burmeister, Head of Buy-Side Products, Risk Analytics,...

© 2013 IBM Corporation

Trends in Economic Capital Modeling

Curt Burmeister

IBM Risk Analytics

Insurance Risk North America

November 5th 2013


Economic Capital Modeling: 2005-present

Phase 1 - Analytics

(2005-2010)

Typical Phase 2

Phase 3 – Reporting

(2010-2015)

2

Complete capital numbers

at the Group and BU level

Used simplified modeling

assumptions where

possible (e.g. curve fitting,

no roll-forward, simple

capital aggregation rules,

no ‘what-if’ runs/reports,

etc.)

Phase 2 –Workflow &

Governance

(2009-2012)

Use active data (i.e. run

model quarterly or other

frequency)

Move to target operating

model (i.e. more

participation from BU

users)

Auditability &

Transparency

‘What-if’ and ad-hoc runs,

additional reporting

Regulatory Reporting

Management Reporting


Economic Capital Modeling: Looking ahead

Phase 4 - Analytics

Typical Phase 2

Phase 6 – Reporting

3

Curve Fitting & Least

Square Monte Carlo

More scenarios

Faster calculations

Reduced IT costs

Improved Credit Risk

Modeling

Phase 5 –Workflow &

Governance

Trusting the numbers

Auditability, Transparency,

Traceability

User annotations and

comments Incorporating “trust

metrics” into risk

management dashboards


Why use 100,000 or more Real World Scenarios?

1. SCR/VaR/CTE convergence

2. Stability of capital attribution

3. Stability of SCR over time (Quarter to Quarter)

“To run just our with-profit model takes an hour, even if we squeeze every bit of efficiency out

of it. To run it 100,000 times would take 10 years”

– Large UK Insurer

… but everyone is looking for lower TCO

4


Proxy the Liabilities

1. Replicating Portfolios

2. Sampling from Empirical & Analytical Distributions

3. Curve Fitting & Least Squares Monte Carlo

5


Curve Fitting / Least Squares Monte Carlo

Loss Function

calibration

A/L Sample

Economic Scenarios

3 2

1

A collection of nested RW

and RN stress scenarios

on relevant risk factors

(MR + NMR).

1

The sample points

must be calculated

under each scenario

in the actuarial

valuation system.

2

Choose a formula (e.g.

polynomial) and a fitting

method (e.g. linear

regression).

Perform the regression,

check goodness of fit

and fine tune.

.

3

8


Curve Fitting

Example

Real World Scenarios = 20

Risk Neutral Scenarios per Real Work

Scenario = 1000

Total Scenarios = 20,000

Note - Real World scenarios are

typically instantaneous shocks

9


Least Squares Monte Carlo

Example

Real World Scenarios = 2000

Risk Neutral Scenarios per Real

World Scenario = 1

Total Scenarios = 2,000

Note - Real World scenarios are

typically 1 year shocks

10


Building the Equations

• Flexible User-Defined Formula: Cross Terms, Squares, Log, etc.

• Piecewise fitting allows to improve local precision.

• Fitting Choice of weights on observations.

• Linear Equations

• a + b * RF1 + c * RF2

• a + b * ln( RF1)

• a + b * Step Function(RF1)

• Non-Linear Equations

• a + RF1* Log(b)

• a * exp(b * RF1)

11


Curve Fitting Example

Liability

– German With Profits

Risk Factors

– German Equity

– German Interest Rate

– Lapse

– Mortality

Value of Liability under 30 Stress Tests

– Partitioned into two Samples of size 15

12


Curve Fitting Equation

c + Constant

a(EQ) + b(IR) + c(Lapse) + d(Mort) + Function of risk factors

e(EQ2) + f(IR2) + g(Lapse2) + h(Mort2) + Function of squared risk factors

i(Lapse*EQ) + j(Lapse*IR) Cross Terms

13


Curve Fitting Example – Summary Statistics

14


Curve Fitting Example – Goodness of Fit

15


Credit Risk


Regulator Feedback

The approach used in modeling credit risk seems overly simplistic, given the size and

complexity of the firm and the methodology appears to have been designed primarily to

deliver an overall group capital figure and does not appear to be capable of playing a key

role in an overall group-wide system for accepting, monitoring and controlling credit risk.

It is unclear if the model is able to provide relevant and required information to stakeholders

within the firm. For example it does not breakdown the credit risk contribution due to spread

only, migration only and default only risks. The firm needs to show that the choice of model

and methodology reflects the risks which the firm believes that it is exposed to and that it

provides sufficiently granular information to ensure that it can play an important role in the

relevant management decisions, at both group and business unit level

The firm should be able to explain links, if any, the firm believes exist between market

conditions and the changes in bond prices, driven by both spreads and migration and

defaults, over the next year.

17


General Framework for Portfolio Credit Risk

19

Scenarios: Market factors 1

x x x x x x x

x

x x

Sampling

LLN

CLT

Idiosyncratic risk & conditional losses

4

FFT

Systemic risks & conditional credit states

3 Obligor exposures 2


Decompose Loses by Risk Type

21

Joint default, migration and spread Spread only

Losses

Probability

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

99.5 99 99.5 99.9

Marginal contributions to loss percentiles

Default

Migration

Spread

Simulate credit loss distributions Analyze risk contributions in expected

and unexpected loss percentiles

Generate a credit loss distribution using Monte Carlo or Sobol Simulation

• Various loss distributions can be generated, such as one based only on spread volatility or

incorporating all spread, migration and default risks.

• Stand alone and Marginal contributions by risk type, scenario, issuer or asset type


Enterprise Risk Governance


Analytics

Production Methodology

Few Know Few Know

Many Consume


Effectively, analytics are to most users a ‘black box’ that they don’t understand.

The Black Square

Director: Hiroshi Okuhara


Many Consume

Few Know Few Know

Instrumented Process

Backtest/Validation

Data Metrics

History

Audits

Control Sets

Quality Indicators

Social Viewpoints

Credibility Score

Point in Time Context

TRUST

NETWORK


RWA – June 2013 – Quality Analysis

050

100150200250300

t-3 t-2 t-1 Today

No. of CalcErrors

No. DroppedPositions

UserAssessment

Timeliness ofData

Level Trace Back System

1 Cognos

2 IRP fact table 16

2 IRP fact table 12

3-12 Data Stage Process Group 13

13 File #382, time stamp XYZ

14-32 Algo One, process 63 time stamp ABC

33 Trading System 1

33 Trading System 2

33 Bloomberg

User 17 on XYZ said:

“The RWA values are unreliable this

month because of a failure in one of the

lending systems to properly convert

currencies. Revised, more accurate

values are expected before end of

August.”

Ref: Remedial Plan 74

More…

RWA Quality

100

50


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Trends in Economic Capital Modeling: Curt Burmeister, Head of Buy-Side Products, Risk Analytics,...

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