1. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com MODELLING AND MEASURING SOVEREIGN CREDIT RISK by Professor Ephraim Clark

2. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Outline u Sovereign vs Corporate Debt u Market Risk vs Credit Risk u Credit Risk Models for Sovereign Debt u Sovereign Debt and Ratings Migrations u Back to the Future –New modelling techniques –Parameter estimation –Country risk derivatives

3. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Sovereign vs Corporate Debt u No recognized legal framework –Zero recovery rates u Willingness vs ability to pay –Difficult to measure u Uncertain maturities –Rescheduling and forgiveness

4. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Market vs Credit Risk (induced by) u Market: vulnerability to external events –interest rates –economic activity u Credit: vulnerability to internal events –Political and social environment –Economic and financial management

5. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Credit Risk Models u Merton type models: structural –contingent claims on borrowers assets –at maturity or some pre-determined barrier –market and credit risk u Jarrow and Turnbull type models: reduced form –Poisson process –doubly stochastic –spread entirely due to credit risk

6. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Structural Credit Risk Models for Sovereign Debt u Gray, Merton, Brodie 2003 –Underlying is FX + Net Fiscal Asset u Karmann and Malritz 2003 –Underlying is FX + PV of expected net exports u Clark 2002 –Underlying is economy’s market value

7. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Reduced Form Models u Several based on Duffie Singleton (1999) –Zhang (2003) with counterparty and issuer risk and 3 state variables tested on Argentina –Merrick (2001) compares Russia and Argentina –Andritzky (2003) similar to Merrick in discreet time, default probabilities and recovery ratios for Argentina u On the horizon: Levy processes for jumps

8. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com 1. The Impact of Rating Changes on Bond Prices u Four basic approaches –Modified duration X change in spread F mixess market and credit risk and assumes no changes in term structure and duration –Event study F mixes market and credit risk F difficult to ascertain correct event date

9. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com 2. The Impact of Rating Changes on Bond Prices – –discount the bond’s cash flows using the new rating class ’s forward zero coupon curve F F mixes market and credit risk F F assumes that yield curves differentials between rating categories are due exclusively to credit risk – –estimate using historical rating drift patterns and observed market spreads of bonds in various rating classes F F neither the spreads nor the drift patterns distinguish between market risk and credit risk

10. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Transition Matrices for Sovereign Debt 1 u Most sovereigns have short ratings histories u Lando and Skodeberg (2001) –Continuous time framework –uses time an obligor spends in a given rating to estimate transition intensities and calculate transition matrix. –Typically give non-zero probabilities for rare events such as from AAA to default

11. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Transition Matrices for Sovereign Debt 2 u Hu, Kiesel and Perraudin (2001) –Probit (latent variable) to model S&P sovereign ratings, used to create ratings F Bayesian updating: combine estimated transition matrix with those of other obligors such as industry –contingency tables: weighted averages of transition matrices obtained in different ways –Typically give positive probabilities for rare events

12. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Modeling Sovereign Financial Risk u Establish accounting discipline u Define income flows u Define expenditure flows u Discounted cash flow to link income and expenditure to the balance sheet

13. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com The Model

14. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Important New Decision Making Parameters u The economy’s international market value u The economy ’s rate of return u The economy ’s volatility

15. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Apply the Information in Black/Scholes

16. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com New Information u Theoretical market value of debt u Theoretical financial risk premium u Maximum debt level u Implied volatility

17. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Sovereign Risk as the Value of the Option to Default u Amount of debt follows GBM u The cost of default can also follow GBM u Value as a real option

18. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com The Unwillingness to Pay

19. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Sovereign Risk as the Value of an Insurance Policy that Pays all Default Losses u Amount of debt follows GBM u Cost of default also follows GBM u Amount at risk includes the option to default u Probability of default follows a Poisson process or a conditional Poisson process

20. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Estimating the Intensity Parameter u Bayesian updating u Bayesian hierarchical modeling u Insurance policies

21. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com The Value of the Insurance Policy

22. Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com Country Risk Derivatives u Volatility swap u Binary option