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Prof. Hugues Pirotte Solvay Business School Université Libre de Bruxelles

Les Journées Bachelier – Journée Risque de Crédit Département de Mathématiques de l’Université d’Evry February 7th, 2003. A Structural Model of the Term Structure of Credit Spreads with Stochastic Recovery and Contractual Design 1999. Prof. Hugues Pirotte Solvay Business School

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Prof. Hugues Pirotte Solvay Business School Université Libre de Bruxelles

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  1. Les Journées Bachelier – Journée Risque de CréditDépartement de Mathématiquesde l’Université d’Evry February 7th, 2003 A Structural Model of the Term Structure of Credit Spreads with Stochastic Recovery and Contractual Design1999 Prof. Hugues Pirotte Solvay Business School Université Libre de Bruxelles Special acknowledgments to Didier Cossin, Hélyette Geman, Rajna Gibson, Eduardo Schwartz, Suresh Sundaresan for their contribution, insights, comments and review on the present paper

  2. Credit Risk Research Environment: Orientations • Mitigation vs Pricing vs Behavioral studies • Structural vs Reduced-Form techniques • Determinants of Credit Risk • Systematic vs specific risk sources • Impact of Macro-variables • Credit vs Liquidity vs Concentration risks • Impact of legal rules/reputation effects on other sanctions • The to components: P(def)+LGD • Credit risk term-structures • Reaction of models to changes in creditworthiness Les Journées Bachelier - Université d'Evry

  3. Credit Risk Research Environment: Uses • Risk in general in Asset Pricing • Corporate Credit Risk • Structural default • Cash-flow insolvency • Sovereign Credit Risk + Firm or Country growth linked to debt levels • Impact of sanctions/Loss of reputation/Cuts in production or exports • Integration of Market and Credit Risks  Portfolio Management Les Journées Bachelier - Université d'Evry

  4. Credit Risk Research Environment: Components • Default Boundary • Exogenous triggers : debt face value • Endogenous triggers : debt service • Recovery-at-default • Ex-ante percentage depending on rating • Variable with some-randomness • Linked to default probability • Endogenously derived • Strategic rules • Identification of a gain in defaulting on purpose! UnwantedDefault Default as an optimal solution Les Journées Bachelier - Université d'Evry

  5. Credit Risk Research Environment: Pricing Models MKT DATA FIRM DATA ECO. DATA Security RATINGS + Legal Treatment of Insolvency Effective Triggers of Distress and Recovery Les Journées Bachelier - Université d'Evry

  6. D F V The Motivation: Ratings as Dynamic Indicators • Priors: • Merton • In the practice: KMV  The option principle applied to a « distance-to-default »  Mapping to ratings following empirical evidence.  « Implementing a Structural Valuation Model of Swap Credit-Sensitive Rates », 1999, H.Pirotte, • Based on a previously published paper in European Financial Management. Les Journées Bachelier - Université d'Evry

  7. Four-Steps Iterative procedure Compute T Compute r(T) Infer V Compute v v E=Call(V,...) T r(T) Les Journées Bachelier - Université d'Evry

  8. Part II: What’s a Structural Model? • The General Idea:  • The problems when defining... • The triggering of the probability of default • The recovery rate • Merton’s idea is, in some respect, less trivial than it appears!(see Crouhy and Galai) Les Journées Bachelier - Université d'Evry

  9. Assumptions of an extended model • Assets’ value dynamics: • Barrier: • Passage time: • Recovery rate definition: • Two-factor interest-ratespecification: Les Journées Bachelier - Université d'Evry

  10. Derivations • Bond price dynamicy (risk-neutral): • With: • Value preservation property: Les Journées Bachelier - Université d'Evry

  11. Derivations (cont’d) • Value of bond at maturity is therefore of the form: • Value of the bond at time 0: Les Journées Bachelier - Université d'Evry

  12. Derivations (cont’d) • With: Les Journées Bachelier - Université d'Evry

  13. Derivations (cont’d) • With: we have ... Les Journées Bachelier - Université d'Evry

  14. Results: debt pricing values Les Journées Bachelier - Université d'Evry

  15. Results: credit spreads • Credit spreadbehavior: Les Journées Bachelier - Université d'Evry

  16. Results: credit spreads (cont’d) Les Journées Bachelier - Université d'Evry

  17. Results: Expected Cost of Default (ECD) • ECD = EPD × ELGD Les Journées Bachelier - Université d'Evry

  18. Results: ECD (cont’d) Les Journées Bachelier - Université d'Evry

  19. Results: ECD (cont’d) Les Journées Bachelier - Université d'Evry

  20. Results: « Rates » Les Journées Bachelier - Université d'Evry

  21. Results: Distance-to-Default Les Journées Bachelier - Université d'Evry

  22. Results: credit spreads vs. maturity Les Journées Bachelier - Université d'Evry

  23. Endogenous choices at time 0! • By absence of arbitrage: • Required credit spread: • Program to be solved: • Equity valuation: Les Journées Bachelier - Université d'Evry

  24. Results Les Journées Bachelier - Université d'Evry

  25. Equity Delta Les Journées Bachelier - Université d'Evry

  26. Les Journées Bachelier - Université d'Evry

  27. Iterating... Les Journées Bachelier - Université d'Evry

  28. Litterature and research fields... • Rationing/Collateral/Mitigation • The option to wait to invest and equilibrium credit rationing; Robert Lensink; Journal of Money, Credit, and Banking, Columbus; Feb 2002; Vol. 34, Iss. 1; pg. 221, 5 pgs • Efficient frontier cutoff policies in credit portfolios; R M Oliver; The Journal of the Operational Research Society, Oxford; Sep 2001; Vol. 52, Iss. 9; pg. 1025 • Using project finance to mitigate telecom risk; Terry A Pratt; Journal of Project Finance, New York; Summer 2001; Vol. 7, Iss. 2; pg. 17 • Modellisation • A pricing model for secondary market yield based floating rate notes subject to default risk; Manfred Fruhwirth; European Journal of Operational Research, Amsterdam; Dec 1, 2001; Vol. 135, Iss. 2; pg. 233 • The term structure of credit spreads with jump risk; Chunsheng Zhou; Journal of Banking & Finance, Amsterdam; Nov 2001; Vol. 25, Iss. 11; pg. 2015 • Counterparty risk and the pricing of defaultable securities; Robert A Jarrow; The Journal of Finance, Cambridge; Oct 2001; Vol. 56, Iss. 5; pg. 1765, 35 pgs • An analytic approach to credit risk of large corporate bond and loan portfolios; Andre Lucas; Journal of Banking & Finance, Amsterdam; Sep 2001; Vol. 25, Iss. 9; pg. 1635 • A Markov chain model with stochastic default rate for valuation of credit spreads; Eiji Kodera; Journal of Derivatives, New York; Summer 2001; Vol. 8, Iss. 4; pg. 8 • Modellisation • Floating-fixed credit spreads; Darrell Duffie; Financial Analysts Journal, Charlottesville; May/Jun 2001; Vol. 57, Iss. 3; pg. 76, 12 pgs Les Journées Bachelier - Université d'Evry

  29. Litterature and research fields... • Basel • Market discipline of banks: The asset test; Donald P Morgan; Journal of Financial Services Research, Dordrecht; Dec 2001; Vol. 20, Iss. 2,3; pg. 195 • Basel Capital Accord implementation delayed; Anonymous; Journal of Taxation of Financial Institutions, Kingston; Sep/Oct 2001; Vol. 15, Iss. 1; pg. 60 • Evaluating the basle guidelines for backtesting banks' internal risk management models; Andre Lucas; Journal of Money, Credit, and Banking, Columbus; Aug 2001; Vol. 33, Iss. 3; pg. 826, 21 • Basel Committee on banking surpervision proposes revision of Basel Capital Accord treatment of credit risk and operational risk; Lawrence A Darby III; Journal of Taxation of Financial Institutions, Kingston; Jul/Aug 2001; Vol. 14, Iss. 6; pg. 76 • The impact of FDICIA and prompt corrective action on bank capital and risk: Estimates using a simultaneous equations model; Raj Aggarwal; Journal of Banking & Finance, Amsterdam; Jun 2001; Vol. 25, Iss. 6; pg. 1139 • Portfolio Management with Credit Risk + Risk Premiums + Products • Basis risk, credit risk and collateralization issues for insurance-linked derivatives and securities; Sylvie Bouriaux; Journal of Insurance Regulation, Kansas City; Fall 2001; Vol. 20, Iss. 1; pg. 94, 27 pgs • Credit risk and the deposit insurance premium: A note; Jean Dermine; Journal of Economics and Business, New York; Sep/Oct 2001; Vol. 53, Iss. 5; pg. 497 • Credit Derivatives • Credit derivatives in banking: Useful tools for managing risk?; Gregory R Duffee; Journal of Monetary Economics, Amsterdam; Aug 2001; Vol. 48, Iss. 1; pg. 25 • Sovereign Credit Risk • Crisis dynamics of implied default recovery ratios: Evidence from Russia and Argentina; John J Merrick Jr; Journal of Banking & Finance, Amsterdam; Oct 2001; Vol. 25, Iss. 10; pg. 1921 • Emerging market debt: Measuring credit quality and examining relative pricing; Robert E Cumby; Journal of International Money and Finance, Kidlington; Oct 2001; Vol. 20, Iss. 5; pg. 591 Les Journées Bachelier - Université d'Evry

  30. Litterature and research fields... • Various empiricals: • Default probabilities in a corporate bank portfolio: A logistic model appraoch; Sjur Westgaard; European Journal of Operational Research, Amsterdam; Dec 1, 2001; Vol. 135, Iss. 2; pg. 338 • An analysis of default risk on residential mortgage loans; Shin-Ping Lee; International Journal of Management, Poole; Dec 2001; Vol. 18, Iss. 4; pg. 421 • The determinants of credit spread changes; Pierre Collin-Dufresne; The Journal of Finance, Cambridge; Dec 2001; Vol. 56, Iss. 6; pg. 2177, 31 pgs • The information content of bank exam ratings and subordinated debt prices; Robert Deyoung; Journal of Money, Credit, and Banking, Columbus; Nov 2001; Vol. 33, Iss. 4; pg. 900, 26 pgs • Firm internationalization and the cost of debt financing: Evidence from non-provisional publicly traded debt; David M Reeb; Journal of Financial and Quantitative Analysis, Seattle; Sep 2001; Vol. 36, Iss. 3; pg. 395, 20 pgs • Estimating corporate yield curves; Antonio Diaz; The Journal of Fixed Income, New York; Sep 2001; Vol. 11, Iss. 2; pg. 95 • Explaining performance trends in leveraged loan investments; Albert J Friedman; The Journal of Fixed Income, New York; Sep 2001; Vol. 11, Iss. 2; pg. 83 • Testing for rating consistency in annual default rates; Richard Cantor; The Journal of Fixed Income, New York; Sep 2001; Vol. 11, Iss. 2; pg. 36 • Unique risk-return characteristics of high-yield bonds; Frank K Reilly; The Journal of Fixed Income, New York; Sep 2001; Vol. 11, Iss. 2; pg. 65 • A balanced approach to forecasting credit risk; Jeffrey S Morrison; The Journal of Business Forecasting Methods & Systems, Flushing; Summer 2001; Vol. 20, Iss. 2; pg. 16, 3 pgs • On the term structure of default premia in the swap and LIBOR markets; Pierre Collin-Dufresne; The Journal of Finance, Cambridge; Jun 2001; Vol. 56, Iss. 3; pg. 1095, 21 pgs Les Journées Bachelier - Université d'Evry

  31. Default probabilities and « Recovery Rates » Les Journées Bachelier - Université d'Evry

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