1. Macrofinancial Risk Analysis Using Contingent Claims Analysis (CCA) for Financial Stability, Linking Financial Sector to Monetary Policy Models Dale Gray Monetary and Capital Markets Department International Monetary Fund Dgray@imf.org 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.

2. 2 Outline Contingent Claims Analysis (CCA) –CCA Framework and Models –Application to Financial Institutions Recent Sub-prime Crisis CCA for Icelandic Banks CCA Models Linked to Factor Models and Monetary Policy Models (application to Chile) Sovereign Economy-wide CCA Models Presentation based on ongoing research Dale Gray; and papers by Dale Gray, Robert C. Merton and Zvi Bodie in: (i) JOIM 2007, (ii) NBER 2007; and (iii) new book on Macrofinancial Risk Analysis (2008).

3. 3 Macrofinancial Risk Analysis Framework integrates risk- adjusted balance sheets using Contingent Claims Analysis (CCA) with macroeconomic and monetary policy models CCA models of financial institutions, corporates, and sovereigns are integrated together and with macroeconomic models

4. 4 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 financial stability Time pattern of CCA risk indicators can be linked to macroeconomic variables and to monetary policy models

5. 5 Core Concept: Merton Model/CCA for Firms and Banks 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.

6. 6 CCA Credit Risk Measures Asset Value Exp. asset Distribution of Asset Value value path Distress Barrier or promised payments V 0 Time Probability of Default T Distance to Distress: standard deviations asset value is from debt distress barrier

7. 7 CCA models of the Financial Sector and links to Macro Models Decomposing factors driving bank CDS spreads –Leverage, asset volatility, Global market risk appetite, loss given default –Implicit put options as a measure of risk Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model

8. 8 Calibrating Implied Assets and Asset Volatility Implied asset value and implied asset volatility calibrated from contingent claims analysis. Merton Model Moody’s-KMV for firms and financial institutions Merton-type CCA or hybrid models have been applied to corporates and financial institutions. Moody’sKMV, Kamakura and others have applied these models for credit risk analysis to tens of thousands of firms and banks in over 50 countries around the world. MKMV provides daily output for 37 financial institutions in Sweden Calibration using equity options Another way to implement the Merton model is to use information from equity options (implied volatility and “skew”) to calculate credit risk and spreads in banks in US, Sweden and other countries.

9. 9 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 Asset Value A and Asset Volatility  A Default Probabilities Spreads, Risk Indicators KMV maps risk indicators to actual default probabilities (EDFs) using historical default data

10. 10 MKMV Key Drivers of Expected Default Frequency (EDF) and EDF Implied CDS spreads (EICDS) EDF Key Drivers are Market Leverage (default point divided by assets) and asset volatility Key Drivers of EICDS are Risk-Neutral EDF (from EDF, Market Sharpe Ratio (SR), correlation ρ) and Loss Given Default

11. 11 What does CCA/MKMV Have to Say About Subprime Crisis? – First, See evolution of market CDS Spreads over the 2007-2008 Crisis for Major US banks and Primary Dealers

12. 12 Market Leverage Has Increased Implied Asset Volatility Has Increased 6/30/2007=100

13. 13 Banks in Subprime Crisis – CCA/MKMV Implied Market Value of Assets, June 30, 2007=100 Assets increase Aug 2007 to early 2008 because of SIV etc. assets brought back on to balance sheets ?

14. 14 EDF Has Increased EDF Implied CDS

15. 15 Significantly Higher Market Sharpe Ratio since July 2007, with peaks on 3/27/08 and 8/6/08 Market Sharpe Ratio and other indicators show decreased risk appetite

16. 16 Changes in Bank CDS due to Leverage, Volatility and Impact of Increase in Market Price of Risk as of March 20, 2008 (Lower Risk Appetite, Higher Correlation) With Subprime Exposure/Loss Without Subprime Loss CDS January 2007 1820 Increased Market Leverage +52+45 Change in Volatility +41+10 Market Price of Risk Increase (SR*ρ) +75+70 CDS March 2008 190 bps145 bps

17. 17 Icelandic banks and government– Questions and issues that CCA can help with What does the equity market vs the CDS market say about credit risk in Icelandic banks? What are implied asset and asset volatility and EDFs? How has the change in global market risk appetite affected CDS spreads in Iceland? What are the differences in credit risk from the equtiy market vs the CDS market? illiquidity of CDS?, What does this mean for the contingent liabilities of the Central Bank (liquidity support) and what does it mean for government?

18. 18 Icelandic Banks CCA Using MKMV

19. 19 Icelandic Banks CCA Using MKMV

20. 20

21. 21 Iceland Banks CCA

22. 22 Iceland Banks CCA

23. 23 Issues regarding differences in information from CDS and Equity markets for Icelandic banks What does the equity market vs the CDS market say about credit risk in Icelandic banks? Take observed market CDS an get implicit Put option (P CDS ) Then take equity information and get implicit Put Option (P EQ ) What are the explanations for the differences? illiquidity of CDS?, illiquidity of equity?, other? What does this mean for the contingent liabilities of the Central Bank (liquidity support) and what does it mean for government?

24. 24 CCA models of the Financial Sector and links to Macro Models Decomposing factors driving bank CDS spreads –Leverage, asset volatility, Global market risk appetite, loss given default –Implicit put options Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model

25. 25 Bank-by-Bank CCA and Factor Models for Stress-Testing Proceedure: 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

26. 26 EXAMPLE OF CHILE BANK FACTOR MODEL - Banks have Heterogeneous Response to Individual Factors; Stress testing can be with individual factors or with Four Principal Components Factors associated with different components of asset returns Factor 1 Factor 2 Factor 3 Factor 4

27. 27 CCA models of the Financial Sector and links to Macro Models Decomposing factors driving bank CDS spreads –Leverage, asset volatility, Global market risk appetite, loss given default –Implicit put options Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model

28. 28 CCA Risk Indicators in Monetary Policy Models The integration of the financial sector vulnerability into macroeconomic models is of keen interest for policymakers. Explicit inclusion of CCA sytemic credit risk/financial fragility indicator Should a financial fragility indicator be included in monetary policy models? –Yes, at least in the GDP Output Gap equation Should it be explicitly included in the reaction function? Or, should the central bank react only indirectly through reacting to its effects on output gap and inflation? –Depends

29. 29 CCA Chilean Banking System Risk and Macro Effects 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.

30. 30 Chilean Banking System – CCA Distance-to- Distress (DTD) is Estimated for Banking System DTD has significant impact on Output Gap

31. 31 DTD related to GDP Growth for Chile Sample: 1998 2007 (monthly) Included observations: 106 after adjustments VariableCoefficientStd. Errort-StatisticProb. C 0.0110.0024.8300.000 R(-1) -0.0010.000-3.7230.000 DLOG(E(-1)) 0.0460.0192.4380.017 DLOG(DTD(-1)) 0.0120.0033.5510.001 DLOG(Y(-1)) 0.4630.0746.2830.000 R-squared 0.574 Mean dependent var 0.009 Adjusted R-squared 0.557 S.D. dependent var 0.013 S.E. of regression 0.008 Akaike info criterion -6.677 Sum squared resid 0.007 Schwarz criterion -6.552 Log likelihood 358.890 F-statistic 34.036 Durbin-Watson stat 1.912 Prob(F-statistic) 0.000

32. 32 DTD related to Output Gap for Chile Sample (adjusted): 1998M02 2007M02 Included observations: 109 after adjustments VariableCoefficientStd. Errort-StatisticProb. C -1.7360.470-3.6910.000 DLOG(TCR(-3),0,3) 4.1341.6392.5220.013 LOG(DTDS(-1)) 0.9340.2563.6530.000 YGAP(-1) 0.5130.0826.2750.000 YGAP(-3) 0.2250.0723.1130.002 R-squared 0.661 Mean dependent var -0.035 Adjusted R-squared 0.648 S.D. dependent var 1.201 S.E. of regression 0.712 Akaike info criterion 2.204 Sum squared resid 52.766 Schwarz criterion 2.328 Log likelihood -115.126 F-statistic 50.695 Durbin-Watson stat 1.842 Prob(F-statistic) 0.000

33. 33 Simple Five Equation Monetary Policy Model GDP Gap with Financial Sector DTD: Traditional Taylor Rule: Taylor Rule with Financial Stability Indicator:

34. 34 Monetary Policy Model (cont.) Inflation: Exchange Rate: Yield Curve:

35. 35 Impulse Response Functions (IRF) with DTD in Monetary Policy Model IRF is the standard tool to analyze the behavior of a monetary model of this type (we are not presenting standard deviations). –For each period of time, the model solves a system of equations for the current and expected value of the main variables; –The model works as expected: signs and magnitudes seem reasonable; –Financial Sector Distance-to-Distress (DTD) has a significant impact on short and long term interest rates, ER, and Output-Gap.

36. 36 Impulse Response: Shock to banking sector distance to default (DTD)

37. 37 Efficiency Frontiers for the steady state volatility of GDP and inflation A base scenario is set where there is no reaction of the monetary policy to DTD, but GDP and exchange rate still react to it. Shocks to DTD could be understood as shocks to risk appetite. Starting from a Base Model a higher reaction to DTD and lower endogeneity are tested.

38. 38 Efficiency Frontiers: Base Model if Monetary Policy Rate reacts to Financial Sector DTD

39. 39 Results and Conclusions of Chile CCA-Monetary Policy Model Analysis A simple, but powerful model for monetary policy including financial sector risk indicator (DTD) Empirical evidence supports the model. DTD affects GDP growth and Output Gap Impulse Responses in accordance with theory. Robust efficient frontier, but there is a trade off in the results: A stronger reaction of policy interest rates to DTD reduces inflation volatility, but increases output volatility. More analysis is being carried out.

40. 40 Unified Macrofinance Framework (Targets: GDP, Inflation, Financial System Credit Risk, Sovereign Credit Risk) Sovereign CCA Model Monetary Policy Model Economic Capital Adequacy Interest Rate Term Structure Model CRIFinancial CCA (Merton-STV) Model (s) Fiscal Policy Debt Management Reserves / SWF Policy Rate Economic Capital Adequacy Bank and Financial Sector Regulations Domestic and International Factors Policies:

41. 41 CCA Model of the Sovereign – Very Useful for Iceland Sovereign Assets –Present value of primary fiscal surplus –Reserves –Minus contingent liabilities to banks and others Sovereign Liabilities –Base money, foreign and local-currency debt –Model measures sovereign spreads Note exchange rate volatility and skew affects sovereign spreads

42. 42 Sovereign, Bank, and Corporate Economy-wide CCA Sector Interlinked Balance Sheets Corporate Sector Assets Sovereign Assets Equity 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 See Annex Implicit Put Option

43. 43 Economy-wide Interlinked CCA Balance Sheets with Assets, Junior Claims, Risky Debt and Cont. Liabilities A=Assets, E=Jr. Claim, B=Def-free Debt, P=Put Options

44. 44 Economy-wide CCA Balance Sheet Models Capture Non-linear Risk Transmission Note that if asset volatility in CCA sector 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 Interlinked implicit options result in compound options that exhibit highly non- linear risk transmission, as seen a variety of financial crises

45. 45 Summary use CCA models of the Financial Sector and links to Macro Models Decomposing factors driving bank CDS spreads –Leverage, asset volatility, Global market risk appetite, loss given default –Implicit put options Vulnerability and stress-testing Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth FX reserves “adequacy” for banking sector contingent liquidity and credit risks Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model

46. 46 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 CCA and the Subprime Crisis (Gray, Merton, Bodie forthcoming) 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; Framework for Integrating Macroeconomics and Financial Sector Analysis by Gray, Karam, Malone, N’Diaye (forthcoming) Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book Foreword by Robert Merton) 202-623-6858 dgray@imf.org

47. 47 Annex 1 - CCA Risk Indicators and Values Value of Risky Debt, D (B=distress barrier, P=implicit put option) D-to-D= Default Probability Risk Neutral DP Estimated Actual DP Credit Spreads

48. 48 Annex 2 - Sovereign, Bank, and Corporate Economy- wide CCA Sector Interlinked Balance Sheets Corporate Sector Assets Sovereign Assets Equity 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 See Annex Implicit Put Option

49. 49 Annex 4 – Aggregation of Credit Risk Indicators (CRIs) Tractable measures of system risk for use with macroeconomic models and for financial stability analysis the CCA credit risk indicators are: Weight the EDF or distance-to-distress for each institution by the implied assets of each bank/financial institution to get a system risk indicator. Use the median or 75% quartile EDF for the sub-sector or group, e.g. as calculated by MKMV. Composite spread or default probability for financial sector, corporate sector and households (if data is available). Weight of the volatility and/or skew from put option on equity of key financial institutions by the assets of the institution. Calculate an Nth to default indicator.Calculate the joint distribution of default probabilities in a portfolio of financial institutions. Tail risk dependence measure from equity options or implied assets is another indicator.