Using Contingent Claims Analysis (CCA) to Measure and Analyze Systemic Risk,

Sovereign and Macro Risk

September 13, 2012

Presentation to Macro Financial Modeling Conference

Dale Gray, IMF, Monetary and Capital Markets Department

The views expressed in this presentation are those of the authors and should not be attributed to the International Monetary Fund, its Executive Board, or its management.

2

Outline of Presentation

Traditional Analysis

Contingent Claims Analysis (CCA)

Applications of CCA:

• Macro Financial CCA: Non-linear Risk Transmission

• Estimating Government Contingent Liabilities

• Systemic Risk Analysis (Application to US)

• Sovereign CCA models and Sovereign-Banking Destabilization Spirals

• Integrated Policy Analysis

3

Outline of Presentation (cont.)

Presentation is based on material in: Gray, D. F., Merton R. C. and Z. Bodie, 2008, “A New Framework for Measuring and

Managing Macrofinancial Risk and Financial Stability,” Harvard Business School Working Paper No. 09-015.

Gray, D., A. Jobst, 2011, “Modeling Systemic Financial Sector and Sovereign Risk,” Sveriges Riksbank Economic Review, September.

As well as:

• Book: Macrofinancial Risk Analysis; other IMF, JOIM, Annual Review of Financial Economics (2009 and 2012) and related papers

• Financial Risk Indicators in Monetary Policy Models (joint work with Central Bank of Chile IMF WP 11/228)

• International Transmission of Macro, Sovereign, Financial, and Corporate Distress (joint work with ECB CCA- GVAR Model of EU)

4

Traditional Analysis is Incomplete

Traditional macroeconomic and banking models do not adequately measure risk exposures of financial institutions and sovereigns and cannot be used to understand the transmission and amplification of risk within and between balance sheets in the economy.

Traditional macroeconomic analysis of the government and central bank is almost entirely flow or accounting balance sheet based. Sovereign debt analyses focus on debt sustainability (stocks, flows and debt to GDP), not sovereign risk exposures (contingent liabilities, expected losses on sovereign debt).

A fundamental point is that accounting balance sheets or a flow-of-funds do not indicate risk exposures, which are forward-looking.

5

CCA Balance Sheet Models and Macroeconomic Models

Macroeconomic models are largely based on flow and accounting balance sheets, 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, DSGE, and other models

6

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

7

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

8

Core Concept of Contingent Claims Analysis (CCA): Merton Model

Assets = Equity + Risky Debt

= Equity + Default-Free Debt – Expected Loss

= Implicit Call Option + Default-Free Debt – Implicit Put Option

Assets

Equity or Jr Claims

Risky Debt

• Value of liabilities derived from value of assets.

• Liabilities have different seniority.

• Randomness in asset value.

9

CCA is Generalization of Black, Scholes, Merton Option Pricing Theory

Liabilities derive their value from assets

Assets are stochastic (changes driven by income flows, asset sales, or changes in value, including credit risk/guarantees)

Uncertain changes in future asset value, relative to the promised payments on debt are the driver of forward-looking values of equity and risky debt.

Risky debt is default-free debt value minus the expected loss due to default which can be measured with an implicit put option.

Key elements are Asset value (A) at time 0, asset return volatility (σ), default barrier (B = PV of promised payments on debt, time horizon (T) and risk-free rate (r).

Note : one does not have to know the expected returns to use CCA/Merton models for valuation of liabilities!

10

Tradeoffs between Market Capitalization, Market Value of Assets and Default Probability (Moody’s KMV data)

CITIGROUP EXAMPLE: From Sept 9, 2008 to March 9, 2009, Market Capitalization fell from $125 bn to $6 bn, 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 Percent

Mar

ket C

apita

lizat

ion

(mill

ion

$)

To get back to a BBB+ rating (0.3% EDF) combinations of capital injection, asset guarantees, debt-equity swaps can

be evaluated; during TARP 107bn in capital was raised

11

CCA is Based on Proven, Well-tested Calibration Techniques

Tools and techniques for calibrating CCA balance sheets of corporates and financial institutions are decades old (as described in HBR 2008 paper). Even commercial sources available (e.g. Moody’sKMV provide CCA risk indicators daily for 40,000 firms and financial institutions in over 60 countries)

Extensions to sovereigns and economy-wide risk transmission is becoming widespread

Over 20 countries have been calibrated; 35 sovereigns; CCA now included in several IMF FSAPs; recent integration into DSGE/monetary policy models and CCA GVAR (Global and EU)

12

As a result of the crisis, CCA concepts have now found their way into the mainstream

The structural CCA model, with its embedded fundamental volatility, endogenously changes as values change (e.g. shocks to assets endogenously change values of equity and risky debt and credit risk premiums)

It helps explain complex risk, especially expected losses in financial system and “insidiousness” of risk exposures where small changes in value can lead to very large changes in risk due to convexity!

13

CCA has robustness

It does not depend on expected returns;

It does not depend on preferences;

It is designed to be modular (can be integrated with many models of consumption and investment);

Retains the (endogenous) non-linearity of values and risk exposures, and can linked to macro models in different ways.

14

For the remainder if my presentation I will describe several ways CCA can be applied to enhance financial stability and macroeconomic analysis

1. Non-linear risk transmission across sectors of an economy

2. Estimating government contingent liabilities

3. Systemic CCA: Measuring Financial Sector Tail-risk Losses And Contingent Liabilities

4. Applying CCA To The Sovereign Balance Sheet; Framework For Sovereign-Bank Feedback Destabilization Processes

5. Unified Macrofinancial Policy Framework

Further Applications

15

1. NON-LINEAR RISK TRANSMISSION ACROSS SECTORS OF AN ECONOMY

Risky debt of households and corporates are assets on financial institution balance sheets and implicit and explicit guarantees of bank’s liabilities are on the sovereign balance sheet

Balance Sheets for the Economic Sectors.

ASSETS LIABILITIES CORPORATE SECTOR

FINANCIAL SECTOR

HOUSEHOLD SECTOR

SOVEREIGN SECTOR (Government and Monetary Authorities)

Source: Gray, Merton and Bodie (2008).

Foreign Currency Reserves

Net Fiscal Asset

(PV of taxes minus expenditures)

Other Public Assets

Financial Guarantees

Foreign-currency Debt

Base Money and

Local-currency Debt

Household Assets (including household income and

savings in the form of deposits and other financial assets)

Net Worth (Subsidiary BS)

Household Net Worth – Claim on Household Assets

Consumption is a “Dividend”

Payment out of Asset Associated With this Claim

Household Real Estate Assets

Household Mortgage and Debt Net Worth (Subsidiary BS)

Loans and other Assets (including loans to corporates, households and sovereign)

Financial Guarantees

Debt and Deposits

Equity

Corporate Assets

Debt

Equity

16

CCA Balance Sheet: Assets Minus Liabilities equal Zero

CCA Balance Sheet

Assets

+or - Implicit or Explicit Guarantees {Implicit Put

Options}

minus

Equity / Jr. Claim {Implicit Call Option}

minus

(Default-free Value of Debt – Implicit Put Option)

= 0

For a sector, sub-sector

or individual institution

17

Stylized Interlinked CCA Balance Sheets for an Economy

Corporates

Households Financial Sector

Sovereign Foreign

H BS H RE Govt. MA Asset

CA

,

FIN

L

H RE

A

A

E

,H REA FA

,

( )

G Other

PV T G

A

,

FX

G

MA Other

R

E

A

ContingentAssets & Liab

FP G FP

Equity/Jr. & Sub. Claims

CE H

H

E

c

,H REE

FE G

SLC SLC

SLC

E

B i

P

BMM

Foreign

Claims

Senior Claims (Default Barrier)

C

C

B

i

,

,

H RE

H RE

B

i

F fB i

SFX SFXB i

Put CP

HP (1 ) FP SFXP

Sum 0 0 0 0 0 0 0

Sectors of an economy can be viewed as interconnected risk-adjusted balance

sheets with portfolios of assets, liabilities, and guarantees—explicit and implicit.

18

Economy-wide CCA Balance Sheet Models Capture Non-linear Risk Transmission

Interlinked implicit options result in compound options that exhibit highly non-linear risk transmission, as seen a variety of financial crises

Note that if asset volatility in CCA balance sheets is set to zero:– 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 macroeconomic flow or accounting frameworks when fundamental structural volatility is ignored (i.e. = 0).

19

Examples of Channels of Risk Transmission

Corporates/Households Banks

Banks Sovereigns

Sovereigns Sov Debt Holders

Financial System Risk GDP Growth

Financial Sector Sovereign

GDP Growth

20

Example of Transmission of Risk from Corporate Sector to Banks to Sovereigns: Case of Thailand

My initial work was motivated to try to understand Asia crisis.

First model was a simple: four corporate sectors, two bank sectors, sovereign model for the Thai economy in the 1990s. Large amounts of foreign debt and pegged exchange rate. This simple model showed:

Corporate risk is embedded in the banking risk. The sensitivity (delta) and convexity (gamma) of banking sector risk increased as the exchange rate depreciates (insidious risk).

21

Example of Transmission of Risk from Corporate Sector to Banks to Sovereigns: Case of Thailand (cont.)

In fact, by using forward exchange rate level and volatility plus balance sheet data (available at the

time), the probability distribution of financial sector losses was 25% of GDP, BEFORE the spot rate moved

from its pegged level!

Actual losses reached around 40% of GDP

22

2. ESTIMATING GOVERNMENT CONTINGENT LIABILITIES AND RISK TRANSMISSION TO SOVEREIGN

Implied credit spreads derived from CCA models (i.e. derived from equity information) are frequently higher than the observed market CDS

This is due to the depressing effect of implicit and explicit government guarantees

The ‘market implied’ guarantees (implicit put option values) can be estimated using CCA and observed CDS

23

Citigroup: Example of Implicit Put Option Value Extracted from CDS vs from CCA model and Estimated

Contingent Liability (billions of US$)

0

100

200

300

400

500

600

700

800

30-Apr-07 30-Apr-08 30-Apr-09 30-Apr-10 30-Apr-11

Implicit Put Option Value from CDS

Implicit Put Option Value from CCA (FVCDS)

0

50

100

150

200

250

300

350

400

450

30-Apr-07 30-Apr-08 30-Apr-09 30-Apr-10 30-Apr-11

Estimated “market implied"

government continent liability

Transfer of Risk: Ireland CDS spreads of banks declined following guarantees in 4Q 2008 and sovereign spread increases

Irish Banks and Sovereign CDS Spreads(In basis points)

0

50

100

150

200

250

300

350

400

Jun-07 Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08

Allied Irish Bank

Bank of Ireland

Irish Government

Source: Bloomberg L.P.

25

Transfer of Risk to Sovereign: Austria Example – CCA Banking Contingent Liabilities vs Sovereign CDS spread

Total Contingent Liabilities vs 5-yr Sovereign CDS Spread

20

40

60

80

100

120

140

160

180

Bil

lio

ns o

f U

S $

0

50

100

150

200

250

300

So

vere

ign

CD

S S

pre

ad

(B

asis

Po

ints

)

Total Contingent Liabilities (simple sum) Sovereign 5-yr CDS Spread

26

Note how CCA financial sector risk indicators (aggregated financial institution CCA indicator related to expected losses) provides:

A robust measure of financial sector systemic risk;

Frequently a leading indicator of credit growth and GDP/output gap;

Provides a quantitative measure of government contingent liabilities, which affects sovereign risk (e.g. spreads)

27

3. SYSTEMIC CCA: MEASURING AND STRESS TESTING FINANCIAL SECTOR TAIL-RISK LOSSES AND CONTINGENT LIABILITIES

Beginning with CCA models of individual banks, expected losses and market implied contingent liabilities

Multivariate extreme value dependence model is then used to calculate the multivariate density of:

(i) the banking system expected losses, and,

(ii) government’s contingent liabilities accounting for the time-varying and non-linear dependence

(iii) measures of financial sector tail risk (95% VaR or Expected Shortfall)

(See Gray and Jobst Swedish Economic Review 2011, and 2009, 2010, & forthcoming)

28

Extreme Tail Risk Total Expected Losses including dependence structure, 36 largest US financial institutions, 95th percentile

0

1,000

2,000

3,000

4,000

Apr

-07

May

-07

Jun-

07

Jul-0

7

Aug

-07

Sep-

07

Oct

-07

Nov

-07

Dec

-07

Jan-

08

Feb-

08

Mar

-08

Apr

-08

May

-08

Jun-

08

Jul-0

8

Aug

-08

Sep-

08

Oct

-08

Nov

-08

Dec

-08

Jan-

09

Feb-

09

Mar

-09

Apr

-09

May

-09

Jun-

09

Jul-0

9

Aug

-09

Sep-

09

Oct

-09

Nov

-09

Dec

-09

Jan-

10

In U

S do

llar b

illio

ns

Total Cont. Liab. (sum of individual expected losses)Total Cont. Liab. (ES, 95th percentile)

LehmanCollapse

Source: IMF US Financial Sector Assessment Program Stress Testing Technical Note 2010

29

Extreme Tail Risk Government Contingent Liabilities including dependence structure, 36 largest financial institutions, 95th percentile

Source: IMF US Financial Sector Assessment Program Stress Testing Technical Note 2010

30

Systemic CCA Shows Nonlinearities of Asset Volatility, Market Capital/Assets, Fair Value Credit Spreads, and Joint Losses – for individual institutions and for the system as a whole (illustrated below)

Aggregate MCAR =Aggregate Market Capitalization/

Aggregate Implied Assets

Aggregate Fair Value Credit Spread

Join

t E

L R

atio

=

Join

t E

xpec

ted

Loss

es (

from

Sys

tem

ic C

CA

)/ A

ggre

gate

M

arke

t C

apita

lizat

ion

Imp

lied

Ass

et

Vo

lati

lity

(Sam

ple

Med

ian)

Systemic Risk Assessment

Jobst and Gray (2012)

31

4. APPLYING CCA TO THE SOVEREIGN BALANCE SHEET; FRAMEWORK FOR SOVEREIGN BANK FEEDBACK DESTABILIZATION PROCESSES

1. Calibrating sovereign balance sheets for emerging market sovereigns with significant foreign currency debt (see Gray, Merton, Bodie 2007 JOIM paper; Gapen et al. IMF Staff Papers 55 #1)

2. Calibrating developed country sovereign balance sheets or government balance sheets in euro area. Calibration uses term structure of CDS/bonds plus debt data to infer sovereign assets, volatility and skew (see Gray, Jobst Swedish Economic Review, page 24 and Appendix 3).

32

Sovereign CCA Balance Sheet, Contingent Liabilities, Joint Bank-Sovereign Stress Testing

Sovereign, or Government, CCA model gives implied sovereign asset value and volatility, whose components can be estimated as shown below:

ASov = Reserves + PV (primary fiscal surplus) – Contingent

Liabilities to Financial sector + Other (residual)

Sovereign spreads = f (sovereign assets, volatility, debt default barrier, time horizon, risk-free rate)

Joint stress testing of banks and sovereigns can be carried out: macro variables affect bank CCA, and thus contingent liabilities, and fiscal surplus and in turn sovereign spreads

(Swedish Economic Review paper shows example on page 24 and 25 of base

and adverse stress test of bank expected losses and sovereign spreads.)

33

Linkages between Stylized Financial Sector and Sovereign CCA Balance Sheets

FINANCIAL SECTOR GOVERNMENT

ASSETSAssets (including government debt)/Loans/Other Assets+ Liquid Assets/Reserves+ Asset Guarantees

Present value of (Fiscal Surplusand Guarantee fees)+ Equity (government owned)+ Other Assets

LIABILITIES - Equity (non-government) - Equity (government-owned)

- Credit owed to Central Bank- Asset Guarantees

- Default-free Debt & Deposits+ (1-α) *Expected Losses due to Default

- α* Expected Losses due to Default

- Present value of Guarantee fees - Default-free Sovereign Debt+ Expected Losses due to Sovereign Default

ASSETS MINUS LIABILITIES0 0

Source: Gray Jobst 2010, and Swedish Economic Review 2011

The circular linkage of bank expected losses and expected losses on sovereign debt can create an insidious destabilization spiral

34

Spillovers from the Sovereign to the Banks and Banks to Sovereigns

DOMESTIC

FOREIGN

SOVEREIGN

BANKS

SOVEREIGN

A. Mark-to-market fall invalue of govt bonds

held by local banks

C. Erosion in potential for official support

D. Mark-to-market fall in value of govt. bonds held by foreign banks

E. Similar sovereigns come under pressure

F. Contagion channels (A, B, & C as above)

G. Rise in counter-party credit risk

H. Withdrawal of funding for risky banksBANKS

B. Increase in bank funding costs

I. Increase in contingent liabilities of govt.

I. Increase in contingent liabilities of govt.

35

CCA Risk Exposures Facilitate Quantitative Analysis of Risk Mitigation Policy Options

Banks:

Increase bank capital higher assets, lower expected losses

Portfolio adjustment/ring-fenced asset guarantees Lower asset volatility

Debt to equity conversion lower default barrier, higher equity

Guarantees on bank debt lower borrowing spreads

Sovereigns:

Increase debt maturity lower default barrier

Fiscal adjustment (“Fiscal Compact”) higher sovereign assets

Guarantees/insurance on sovereign debt lower sovereign spreads

Supranational:

Debt purchases by public entity (ECB, EFSF, ESM, other) lower sovereign spreads

Eurobonds lower sovereign spreads, risk diversification

36

5. 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

37

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 Accounting

Balance Sheet(s)

Corporate Accounting

Balance Sheet(s)

Capital Injections

Global Market Flows

Credit Flows

38

FURTHER APPLICATIONS – New risk-adjusted GDP and external account measures (from economy-wide CCA balance sheets, slide 17)

Solving for the put option in the financial sector one can see the put option depends on the implicit put options in other sectors. It is the compound nature of this put option which can lead to sudden non-linear increases in value.

( ) ( ) ( )F F F F F F DCF C C DLCF GLC GLC DH H HP E B A E B B P B P B P

Combining all the components of the junior claims or call option values across the economy (households, government, and foreign sector) gives the CCA-based Economic Output

CCAEO = 1 ... H j H n H G EC C EF FE E E E f E f E .

The sum of all foreign claims across the sectors is defined as the risk adjusted external account.

( )

( (1 ) ) ( )EC C EF F DC C C

DF F F GLCH GLC GLC

Risk Adjusted External Account f E f E f B P

f B P f B P

See Gray, D. F., Jobst, A. A., and S. Malone, 2010, “Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth,” Journal of Investment Management

39

FURTHER APPLICATIONS (cont.) - Integrating Financial System Risk Indicators into Monetary Policy ModelsGDP 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; Explicit inclusion of CCA banking system credit risk

indicator in monetary policy models in the output gap equation.

Uses a simple two-module framework:

1. Central Bank of Chile Macro Monetary Policy Model.

2. CCA Financial System Module. See Garcia et al. 2011 “Incorporating Financial Sector into Monetary Policy Models: Case

of Chile” IMF WP/11/228

40

Including CCA Banking Risk Indicator in Bank of Chile Monetary Policy Model: Conclusions

A simple, but powerful model for monetary policy including financial sector risk. Empirical evidence supports the model. Impulse Responses behave according to theory.

Robust efficient frontier (inflation volatility vs output volatility) A stronger reaction of interest rates to financial risk indicator reduces inflation volatility and output volatility.

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

vol

atili

ty

DTD: 0.5

DTD: 1.0

DTD: 1.5

41

FURTHER APPLICATIONS (cont.) - Ongoing Joint work with ECB – CCA-GVAR for EU(Joint work with ECB: Marco Gross, Matthias Sydow, and Joan Paredes)

Framework for analysis the interactions of banking sector risk, sovereign risk, GDP growth, stock markets, and other macro variable for 15 EU countries plus the US.

Uses CCA risk indicators for the banking systems and corporate sectors and sovereigns in each country,

Together with the GVAR (Global Vector Autoregression) model for each country, and weight matrices, impulse responses captures the non-linearity of changes in bank assets, equity capital, bank credit spreads, sovereign spreads and corporate credit risk.

42

CCA-GVAR model framework

CCA bank by bank risk indicators (63)

CCA sovereign credit risk indicators (16)

GDP data (16 series) Stock market index (16)

Other

Copula Simulation

GVAR Model (16 local

country models)

Scenarios and Shock Origins

Weighting Matrices

CCA banking system risk indicators (16)

Scenario Responses

GDP growth IRs Stock market IRs

Banking system IRs (ELRs and spreads)

Sovereign IRs (ELRs and spreads)

EU and Euro Zone Aggregate banking and sovereign

debt expected losses Aggregate bank capital impact

Sovereign Module Sovereign output results :

- Expected Losses - Credit Spreads - Other

Banking Module Banking system responses

Bank by bank output results :

- Funding cost impacts - Expected Losses - Implied market capital

impact - Government

contingent liabilities

Fiscal and Growth Module

- Contingent liabilities - Borrowing cost changes - Debt to GDP changes

43

Conclusions for CCA GVAR Model

Integrated forward-looking banking system, corporate and sovereign risk indicators in a GVAR with macroeconomy and financial markets;

Large panel of banks, sovereigns, macro, financial markets all fully endogenous;

Stable global model provides meaningful responses in terms of directions and magnitude;

CCA captures nonlinear features related to bank capital, funding cost and sovereign risk;

Allows a range of policy options to be modeled and their risk mitigation impact quantified.

44

Additional references:

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

Gray, Dale F., Robert C. Merton, and Zvi Bodie. (2006) “A New Framework for Analyzing and Managing Macrofinancial Risks of and Economy” Harvard Business School Working Paper, No. 07-026, 2006. (Also NBER Working Paper Series, No. 12637.)

Gray, D. F., Merton R. C. and Z. Bodie, 2007, “Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk, Journal of Investment Management, Vol. 5, No. 4, pp. 5-28.

Gapen M. T., Gray, D. F., Lim C. H., Xiao Y. 2008, “Measuring and Analyzing Sovereign Risk with Contingent Claims,” IMF Staff Papers Volume 55 Number 1 (Washington: IMF).

Gray, D. F., Jobst, A. A., and S. Malone, 2010, “Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth,” Journal of Investment Management, Vol. 8, No. 2, pp. 90-110.

Chen, Q., D. Gray, P. N’Diaye, H. Oura 2010 “International Transmission of Bank and Corporate Distress” IMF Working Paper No. 10/124 (Washington: International Monetary Fund).

Garcia, C., D. Gray, L. Luna, J. Restrepo, 2011, “Incorporating Financial Sector into Monetary Policy Models: Application to Chile,” IMF WP/11/22

Gray, D. and S. Malone, 2012, “Sovereign and Financial Sector Risk: Measurement and Interactions” Annual Review of Financial Economics, 4:9.

Gray, D., M. Gross, J. Paredes, M. Sydow, 2012, “Modeling the Joint Dynamics of Banking, Sovereign, Macro, and Financial Risk using Contingent Claims Analysis (CCA) in a Multi-country Global VAR” forthcoming

Gray, D. F., and A. A. Jobst, 2012, “Systemic Contingent Claims Analysis (Systemic CCA) – Estimating Potential Losses and Implicit Government Guarantees to Banks,” IMF Working Paper (Washington: International Monetary Fund), forthcoming.