New Framework for Analyzing Macrofinancial Risk and Financial

Stability: Contingent Claims Approach

Presentation at the Bank of Thailand

October 6, 2009

Dale Gray

Sr. Risk Expert

Monetary and Capital Markets Department

International Monetary Fund

The views expressed in this presentation are those of the author and should

not be attributed to the International Monetary Fund, its Executive

Board, or its management. The presenter’s email is dgray@imf.org

2

Macrofinancial Risk Linkages

Macroeconomic

Models

Monetary Policy

Models

Risk-Adjusted

Balance Sheet Models

(Corporate, Financial,

and Sovereign Sectors)

3

Macrofinancial Risk Analysis

� Framework integrates risk-

adjusted balance sheets

using Contingent Claims

Analysis (CCA) of financial

institutions, corporates,

and sovereigns together

and with macroeconomic

and monetary policy

models

� TOOLKIT FOR MACRO RISK

ANALYSIS

4

Outline

I Risk-Adjusted Balance Sheets: The Contingent Claims Analysis (CCA) Framework

• Economy-wide Interlinked Balance Sheets

• Towards Unified Framework for Policy

II Application of CCA to Corporates and Financial Institutions

• Default Probability;

• Stress Testing; Capital Adequacy

• Systemic Risk Analysis

• Impact of Financial Guarantees on Banks and Sovereign Risk

• Integrating CCA Models into Monetary Policy Models

5

Part I Risk-Adjusted Balance Sheets: The

Contingent Claims Analysis (CCA)

Framework

6

Core Concept: Merton Model (CCA) for Firms and Banks

Assets = Equity + Risky Debt

= Equity + PV of Debt Payments – Expected Loss due to Default

Assets

Equity or Jr Claims

Risky Debt

• Value of liabilities derived from value of assets

• Uncertainty in asset value

Note: Measured using option valuation formulas

7

CCA Credit Risk Measures

Asset Value

Exp. asset Distribution of Asset Valuevalue path

Distress Barrier or promised payments

V 0

Time

Probability of Default

T

Distance toDistress: standard

deviations asset value is from debt distress

barrier

8

Example for a Thai Corporate

If Assets, at time 0, = 250 bn baht

Volatility of Asset return =15% (annual)

Promised payments on debt = 100 bn baht

This gives:

Default Probability is 0.2% over one year and associated rating is A+

But assets and asset volatility can’t be observed directly: How can they be calculated?

9

Estimating CCA Risk-adjusted Balance Sheets for Financial Institutions and Corporates

If equity is traded in the market, CCA uses forward-looking equity information plus balance sheet data

– Inputs:

• Value and Volatility of Market Capitalization

• Debt Distress Barrier (PV of promised debt payments, from book value)

– Outputs:

• Implied Market Value of Assets and Asset Volatility,

• Default Probability, Expected Losses due to Default, Credit Spread and other Risk Indicators

If there is not traded equity, direct estimation of assets and asset volatility can be used instead

10

Calibrate (Unobservable) Market Value of Asset and Implied Asset Volatility

INPUTS

� Value and Volatility of Market Capitalization, E

� Debt Distress Barrier B (from Book Value)

� Time Horizon

USING TWO EQUATIONS WITH TWO UNKNOWNS

Gives:

Implied Market Value of Assets

and

Asset Volatility

Default Probabilities

Spreads, Risk Indicators

11

Macrofinancial Risk Analysis is Applied at Bank, Sector, and Economy-wide Levels

CCA risk analysis tools can be applied to

measure, analyze and manage risk for:

(i) Financial sector

- Individual Institutions

- System of Institutions

(ii) Corporates and Corporate Sectors

(ii) Sovereigns

(iv) Households

(v) Economy-wide Risk Framework

12

Sovereign, Bank, and Corporate and Household

Economy-wide CCA Sector Interlinked Balance Sheets

Corporate and Household Sector

Assets

Sovereign

Assets

Equity/NW

Default-free Debt Value

– Put Option

Money &

Local Currency Debt

Foreign Def-free Debt Value – Put Option

Banking/ Financial

Sector Assets

Deposits and Debt Value –Put Option

Equity

Contingent Liab

Risky Debt = Default-free Value of

Debt minus Expected Losses

Expected losses in risky debt are

implicit put options, contingent

liabilities are implicit put

options, equity and junior claims

are implicit call options

Implicit Put Option

13

CCA Balance Sheet Models Capture Non-linear Risk Transmission

� Note that if asset volatility in CCA balance

sheets is set to zero:

– All implicit put options go to zero,

– Macroeconomic accounting balance sheets and

traditional flow-of-funds are the result

– Measurement of (non-linear) risk transmission is

not possible using flow-of-funds or accounting

frameworks

� Traditional macroeconomic accounts do

not include risk!

14

Linking CCA Balance Sheet Models to Macroeconomic Flows and Models

� Macroeconomic models geared to try to forecast

the mean of macro variables (i.e. first moment)

� Finance measures risk from stochastic assets

relative to threshold (second and third moments

critical to risk indicators).

� CCA is an excellent tool for analyzing

macrofinancial linkages

� Time pattern of CCA risk indicators can be linked

to macroeconomic variables and to monetary

policy models

15

Added Dimension of Risk Indicators CCA Risk Analytics Models to Spectrum of Macroeconomic Models

Risk Analytics Models CCA, Credit Risk Macroeconomic Theory Based RBC, GE IS-LM DSGE, MPM VAR Data Based Macroeconomic Models

16

Where we ultimately want to go…….

Unified Macrofinancial Policy Framework

� Financial Stability Policies

� Monetary Policy

� Fiscal, Reserve and Debt Management

Policies

17

Unified Macrofinance Framework Targets: Inflation, GDP,

Financial System Credit Risk, Sovereign Credit Risk

Sovereign CCA Balance

Sheet Model

Monetary Policy Model

Interest Rate Term Structure

Financial System Credit Risk IndicatorFinancial

Sector CCA Model

• Fiscal Policy

• Debt Management

• Reserve Management

• Policy Rate

• Liquidity Facilities

• Quantitative Actions

• Capital Adequacy

• Financial Regulations

• Economic Capital

Fiscal and Debt Policies:

Guarantees

Financial Stability Policies:

Sovereign Credit Risk Indicator

Monetary Policies:

Household CCA

Balance Sheet(s)

Corporate Sector CCA Balance Sheet(s)

Sovereign Equity Claims (from Capital Injections)

Global Market Claims on

Sovereign

18

Traditional Flow and Accounting Framework No Risk-Adjusted Balance Sheets (Asset Volatility = 0)

No Credit Risk or Guarantees; No Risk Exposures

GovernmentAccounts Flow of Funds

Monetary Policy Model

Interest Rates

Bank Accounting Balance Sheets

• Fiscal Policy

• Debt Management

• Reserve Management

• Policy Rate

• Liquidity Facilities

• Quantitative Actions

• Capital Adequacy

• Financial Regulations

Fiscal and Debt Policies:

Financial Stability Policies: Monetary Policies:

Household AccountingBalance Sheet(s)

Corporate AccountingBalance Sheet(s)

Capital Injections

Global Market Flows

Credit Flows

19

Part II Application of CCA to Corporates

Financial Institutions and Systemic Risk

20

II. Application of CCA to Corporates and Financial Institutions

Examples for Two Thai Corporates (Moody’sKMV Model)

Large Thai Corporate

Asset 246 bn baht

Asset volatility 14 %

Default barrier 102 bn baht

Default Prob (EDF) 0.15%

Credit Spread 265 bps

Small Thai Corporate

0.35 bn baht

50 %

0.14 bn baht

4.2 %

1320 bps

21

Median (50th Percentile) Corporate Sector Default Probability for the last 2 years (up to Oct 1, 2009)

0

2

4

6

8

10

129/

30/2

007

10/3

0/20

07

11/3

0/20

07

12/3

0/20

07

1/30

/200

8

2/29

/200

8

3/30

/200

8

4/30

/200

8

5/30

/200

8

6/30

/200

8

7/30

/200

8

8/30

/200

8

9/30

/200

8

10/3

0/20

08

11/3

0/20

08

12/3

0/20

08

1/30

/200

9

2/28

/200

9

3/30

/200

9

4/30

/200

9

5/30

/200

9

6/30

/200

9

7/30

/200

9

8/30

/200

9

9/30

/200

9

One

Yea

r D

efau

lt P

roba

bilit

y in

Per

cent

...

THAILAND CORPORATES GROUP

INDIA CORPORATES GROUP

MALAYSIA CORPORATES GROUP

HONG KONG CORPORATES GROUP

JAPAN CORPORATES GROUP

US CORPORATES GROUP

SINGAPORE CORPORATES GROUP

22

50

55

60

65

70

75

80

85

90

95

100

0 5 10 15 20 25 30 35

1-year EDF (%)

Per

cent

age

of C

umul

ativ

e A

sset

s

1/9/2007

9/1/2008

3/18/2009

Thailand Corporate Sector – Cumulative Assets vs

Default Probability

23

CCA Model for Banks

Examples for Two Groups of Thai Banks (Moody’sKMV Model)

Large Banks (average)

Asset 1200 bn baht

Asset volatility 3.9 %

Market Cap 180 bn baht

Default barrier 914 bn baht

Default Prob (EDF) 0.1%

Credit Spread 110 bps

Small Banks (average)

120 bn baht

6.7 %

11.5 bn baht

96 bn baht

0.75 %

340 bps

24

50th Percentile Default Probability for Banking Groups for the last 2 years (up to Oct 1, 2009)

0

1

2

3

4

5

6

7

9/30

/200

7

10/3

0/20

07

11/3

0/20

07

12/3

0/20

07

1/30

/200

8

2/29

/200

8

3/30

/200

8

4/30

/200

8

5/30

/200

8

6/30

/200

8

7/30

/200

8

8/30

/200

8

9/30

/200

8

10/3

0/20

08

11/3

0/20

08

12/3

0/20

08

1/30

/200

9

2/28

/200

9

3/30

/200

9

4/30

/200

9

5/30

/200

9

6/30

/200

9

7/30

/200

9

8/30

/200

9

9/30

/200

9

One

Yea

r D

efau

lt P

roba

bilit

y, P

erce

nt.

THAILAND BANKS GROUP

INDIA BANKS GROUP

MALAYSIA BANKS GROUP

JAPAN BANKS GROUP

UNITED STATES BANKS GROUP

25

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09

Ratio of Implied Market Value of Assets to Liabilities for Example Banks

Default zoneLehman

JPMorgan

Citigroup

26

CCA Models are useful because they:

� measure credit (default) risk

� link equity value and volatility to credit

spreads

� CCA is useful not just to analyze default

risk, but risk of declining below any

barrier, e.g. minimum capital /prompt

corrective action barrier for banks, or

risk of declining from AA rating to BBB

rating, etc.

27

Some Applications of CCA models:

Stress-testing with CCA plus Factor Model

Quantitative assessment the impact of government interventions and unwinding (capital adequacty debt and asset guarantees, etc.)

“Systemic CCA” used to determine systemic tail-risk in the banking system and government contingent liabilities.

Risk transfer from financial sector to the sovereign

Integrating financial sector into monetary policy models

28

EXAMPLE: Bank-by-Bank CCA and Factor Models for Stress-Testing

Procedure:

� Calibrate CCA model for each bank

� Estimate factor model for bank return

� Generate scenarios and carry out stress test to see impact on bank credit risk and on equity capital

Step 1 Step 2 Step 3 Step 4

Scenario generation (global and domestic factors)

Factor Model for bank asset return (or bank risk indicators)

CCA model for each bank (or bank group)

Impact on bank credit risk, (POD, implicit put, spread) and on equity capital

Gray, D. and J. Walsh (2007) “Factor Model for Stress-testing

with a Contingent Claims Model of the Chilean Banking

System.” IMF Working Paper 08/89.

29

EXAMPLE OF CHILE BANK FACTOR MODEL - Banks have Heterogeneous Response to Individual Factors; Stress testing canbe with individual factors or with Four Principal Components

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6

VIX Chile CPI IMACEC Chile Unemp.S&P Yld Curve 10-Yr (Chg) Oil Chile CPI CLP / BRLIPSA 1-Yr (Lvl) 1-Yr (Chg) Copper Copper

CLP / USD US CPI

Financials Cyclicals Domestic Domestic/(Levels) Change Regional

U.S. Rates

U.S. Rates

Factors associated with different components of asset returns

Factor 1 Factor 2 Factor 3 Factor 4

0%

1%

2%

3%

4%

5%

6%

7%

1 4 7 10 13 16

Scenario 1: Shock to Financials Variable Comparable to 2003

Defau

lt Pro

bability

30

Key Points on Using CCA for Policy

� CCA + Factor Model provides “CCA Early Warning Stress Testing System”

� CCA + VAR models can capture macroeconomic, corporate and banking sector feedback effects

� Useful for Economic Capital Adequacy CCA can be used to measure cost and benefits of:

– Financial guarantees and deposit insurance (can be used to estimate the proper guarantee fee to be charged)

– Risk transfer to sovereign

– Combinations of policies (capital adequacy, liability guarantees, asset guarantees, other)

31

Tradeoffs between Market Capitalization, Market Value of Assets and Default Probability

Citigroup Example: From Sept 9, 2008 to March 9, 2009, Market Capitalization fell from $125 bn to $6, Assets declined and Default Probability went from 0.5% to 24%

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

1,400,0001,500,0001,600,0001,700,0001,800,0001,900,0002,000,0002,100,000

Market Value of Assets (million $)

Mar

ket C

apita

lizat

ion

(mill

ion

$)0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

0 5 10 15 20 25 30

EDF, One Year Default Probability in PercentM

arke

t Cap

italiz

atio

n (m

illio

n $)

Changes in market cap (common equity) affect

default in a non-linear way

32

In April 2009, Possible Strategies to get to Citigroup to a Target Default Probability of say 0.3% (=BBB+ rating)

Option 1 – Capital Injection: Increase market

capitalization by $ 99 bn

Option 2 – Asset Purchase and/or Ring-fenced

Asset Guarantee which lowers asset volatility

by 10% plus increase market capitalization

by $65 bn

Option 3 – Reduce short-term liabilities by

$140 bn (voluntary debt for equity swap)

plus reduce volatility by 10% plus increase in

capital by $18 bn

33

After Stress-tests Citigroup raised common equity (market cap) back to up to $107 bn

Default probability went from 25% down to 0.3% by Sept 2009

0

20000

40000

60000

80000

100000

120000

140000

1,400,0001,600,0001,800,0002,000,0002,200,000

Market Value of Assets (million $)M

arke

t Cap

italiz

atio

n

0

20000

40000

60000

80000

100000

120000

140000

0 5 10 15 20 25 30

EDF One Year Default Probabilitiy Percent

Mar

ket C

ap

34

Systemic CCA

Systemic risk is ultimately about fiscal liabilities

But market-based indicators net out guarantees (or cost expected to be borne by government)

Here, computing implicit put options (expected losses) from equity markets (rather than debt markets) to split risk borne by government vs. risk retained by banks

(preliminary results for US from Gray and Jobst, 2009)

35

Implied CDS spreads are much higher than observed CDS spreads, which are net of government liability guarantees

(Gray, Merton, Bodie 2008 and Gray and Jobst 2009)

Government contingent liability = αααα*implicit put option derived from bank equity

Value of put option on CDSα = 1 -

Value of put option on equity

Assets = Implicit Call Option + [Default-Free Debt – (1-

α)*Implicit Put Option] – α*Implicit Put Option

Using CCA with equity information and information

from CDS spreads allows us to calculate the share

of risk born by the government

36

Systemic CCA

Multivariate extreme value dependence model is then used to calculate the multivariate density and thus the government’s contingent liabilities accounting for the time-varying and non-linear dependence (correlation)

37

US Systemic CCA Model (preliminary analysis)Simple Sum of Contingent Liabilities to Banks (gray area) vs50th Percentile from Multivariate Distribuiton(Jobst, 2009, Gray and Jobst 2009)

US Financial Sector Systemtic CCA - Simple Sum of Contingent Liabilities vs 50th Percentile of Multivariate

Density of Contingent Liabilities 1/

0

500

1,000

1,500

2,000

2,500

26-Jun-

08

10-Jul-

08

24-Jul-

08

07-Aug-

08

21-Aug-

08

04-Sep-

08

18-Sep-

08

02-Oct-

08

16-Oct-

08

30-Oct-

08

13-Nov-

08

27-Nov-

08

11-Dec-

08

25-Dec-

08

08-Jan-

09

22-Jan-

09

05-Feb-

09

19-Feb-

09

05-Mar-

09

19-Mar-

09

02-Apr-

09

16-Apr-

09

30-Apr-

09

14-May-

09

28-May-

09

In U

S d

oll

ar

bil

lio

ns

Total Contingent Liabilities (simple summation of avg. individual contingent liabilities)

Total Contingent Liabilities (average univariate marginals, GEV, 50th percentile)

Sample period: 06/26/2008-06/10/2009 (271 obs.) of individual contingent liabilities of sample banks. Source: IMF staff estimates. 1/ The multivariate density is generated from univariate marginals that conform to the Generalized

Extreme Value Distribution (GEV), estimated via the Linear Ratio of Spacings (LRS) method over an estimation window of 30 days, and a non-parametric identification of the time-varying dependence structure.

38

Example of Systemic CCA Applied to Group of Banks Country to Analyze Systemic Tail-Risk (preliminary analysis)

Contribution banks identified as needing more capital (red) to

multivariate contingent liabilities of US government at the 99th

percentile and those banks not needing more capital (green)

39

Estimation of Government Contingent Liabilities

Explicit or implicit government guarantees

mean the government is taking over part of

the banks’ Expected Loss due to Default

Assets =

Equity + PV of Debt Payments – Expected Loss due to Default

Government’s share of Expected Loss due to Default are the Government’s contingent liabilities

40

Risk Transfer to Sovereign Balance Sheet

� Financial Guarantees Raise Expectation of

Higher Fiscal Costs which Reduces Sovereign

Assets, can increase Sovereign Spreads

� Sovereign CCA Model*:

ASov = Reserves + PV (primary fiscal surplus)

+ Other – Contingent Liabilities

*See JOIM paper December 2007 (Gray, Merton, Bodie) and IMF Staff Papers March 2008

41

Ireland Example is Dramatic – After Bank Debt Guarantees, Bank CDS decreases and sovereign CDS increases.

0

50

100

150

200

250

300

350

400

1 21 41 61 81 101 121 1410

50

100

150

200

250

300

350

400

Allied Irish Bank

Bank of Ireland

Sovereign

42

20

40

60

80

100

120

140

160

180

Jul-08 Oct-08 Jan-09 Apr-09

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

Higher Contingent Liabilities Can Increase Sovereign Risk

Country Example: contingent liabilities are correlated and lead the sovereign default probability (inferred from sovereign CDS

spreads)

Total contingent liabilities(LHS, US$bn)

Est. sovereign default prob. 1-year(RHS, %)

43

Incorporating Financial Sector Risk into Monetary Policy Models

GDP is affected by financial stability in the banking system via

� Financial accelerator links;

� Financial distress in banks and bank’s borrowers reduces lending as borrower’s credit risk increases, which reduces investment and consumption affecting GDP.

� Explicit inclusion of CCA systemic credit risk/financial fragility indicator captures financial accelerator and crisis periods.

44

How can a system financial fragility indicator be included in monetary policy models?

– In the GDP Output Gap equation

45

Chilean Example – CCA banking system risk indicator is related to Output and Output Gap

-6

-4

-2

0

2

4

6

8

10

12

Jun-97 Jun-00 Jun-03 Jun-06

DTD of Banking System

Output Annual Growth

Output Gap

Distance to Distress (DTD) for the Chilean Banking System, Output and Output Gap

-6

-4

-2

0

2

4

6

8

10

12

Jun-97 Jun-00 Jun-03 Jun-06

DTD of Banking System

Output Annual Growth

Output Gap

DTD has significant and positive

impact on output gap

46

Monetary Policy + CCA Model

Uses a simple two-module framework:

1. Macro Monetary Policy Model.

2. CCA Financial System Module.

This macro model includes the financial stability/ credit risk indicator (banking system distance to distress) in the output gap equation and the exchange rate equations.

47

What happens if Interest Rates react to the

banking sector fragility indicator: Including

DTD in the policy rule reduces inflation

volatility and output volatility

The size of the reaction to DTD in the Taylor rule has a very significant effect on the

results. Indeed The larger the coefficient associated to DTD in the authorities

reaction function, the closer to the origin is the frontier obtained with the

simulations (orange line in Figure below).

Base model reaction to dtd: 0.5, 1.0 ,1.5

2.0

3.0

4.0

5.0

6.0

3.0 4.0 5.0 6.0 7.0

Inflation volatility

Out

put v

olat

ility

DTD: 0.5

DTD: 1.0

DTD: 1.5

48

Summary

CCA incorporates risk-adjusted balance sheets and credit risk into macro and financial stability analysis

Numerous Applications, such as:

� Early warning

� Stress testing

� Assessing quantitative impact of capital raising and government policy interventions in the financial system

� Systemic CCA calculates contribution of banks to tail risk and can be used to set systemic risk charges

� Analysis of risk transfer to the sovereign

� Model for including financial sector risk in monetary policy models

49

Thank you, More information see :

Papers by D. Gray, Robert C. Merton, Zvi Bodie:

� NBER 12637 (2006)

� NBER 13607 (2007)

� Sovereign Credit Risk, JOIM v. 5, no. 4, Dec 2007

� HBS WP 09/015 August 2008

� CCA and the Subprime Crisis (Gray, Merton, Bodie) found at:

www.greta.it/credit/credit2008/Tuesday/06_Bodie_Gray_Merton.pdf

IMF Working Papers: WP 05/155, 04/121, 07/233, Indonesia SIP (2006), Gray and Walsh (WP 08/89), Gray, Lim, Loukoianova, Malone (WP/08), IMF Staff Papers Gapen et. al v 55 #1 2008;

Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book Foreword by Robert Merton)

Annual Review of Financial Economics 2009 “Modeling Financial Crises and Sovereign Risk” by Dale Gray

202-623-6858 dgray@imf.org

50

Parallels between Explicit and Implicit Option Prices

A=E+B-ELS=C+K-PNote put call

parity relation

Expected credit

loss on debt (EL)

Explicit put

option value (P)Put Option

Equity or junior

claim (E)

Explicit call

option value (C)Call Option

Debt distress

barrier (B)

Strike price of

option (K)Strike Price

Asset on balance

sheet (A)

“Asset” such as

stock price, FX,

etc. (S)

Underlying

“Asset”

CCA Implicit

Option Prices

Explicit

Option Prices

51

Simplest Description of Option Values with a “Stochastic or Uncertain” Asset

Assets = max (A-B,0)

Be-rt - max(B-A,0)

Call Option = Equity = max (A-B,0)

Risky Debt =Be-rt - max(B-A,0)

Put Option = max(B-A,0)

(Note, if the asset A is not stochastic, i.e. it has no volatility,

then in a balance sheet context, the put option goes to

zero and the call option turns into the “accounting balance

sheet” or “net worth balance sheet”)