Recovery of Market Value

1. Recoveryof Market Value Andreas Gerwinski Seminar CreditRisk Dr. Frank Seifried TU Kaiserslautern 17.Januar 2011

2. Content • Chapter 1: Valuationofdefaultable Claims • a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate • Chapter 2: ValuationofDefaultable Bonds • Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds • Chapter 3: Pricing Bond andCredit Derivatives • Pricing a credit-spread put option D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

3. Content • Chapter 1: Valuationofdefaultable Claims • a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

4. Valuationofdefaultable Claims • modeling term structures of bonds and other contingent claims that are subject to default risk • default as an unpredictable event governed by a hazard rate process • parameterization of losses at default in terms of the fractional reduction in market value that occurs at default • fix some contingent claim that, if no default occurs, pays X at time T • Arbitrage-free setting in which all securities are priced in terms of some short-rate process r • and equivalent martingale measure Q • Under this “risk neutral” probability measure, • fractional loss in market value if default were to occur at time t, • conditional on the information available up to time t • this claim may be priced as if it were default-free by replacing the usual short-term interest rate process r with the default-adjusted short-rate process R=r +hL D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

5. Valuationofdefaultable Claims Valuationequationorgeneralpricingrelation D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

6. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

7. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

8. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

9. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

10. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

11. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

12. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

13. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

14. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

15. a discrete-time Motivation • Continuous-time valuation • Exogenousexpectedloss rate • a continuous-time Markovformulation • Price dependentexpectedloss rate Valuationofdefaultable Claims D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

16. Content • Chapter 2: ValuationofDefaultable Bonds • Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

17. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

18. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

19. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

20. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

21. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

22. Recoveryandvaluationofbonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

23. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

24. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

25. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

26. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

27. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

28. Recoveryandvaluationofbonds • Valuation of noncallable corporate bonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

29. Recovery and valuation of bonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuationofdefaultablecallablebonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

30. Recovery and valuation of bonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuation of defaultable callable bonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

31. Recovery and valuation of bonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuation of defaultable callable bonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

32. Recovery and valuation of bonds • Valuationofnoncallablecorporatebonds • a defaultable HJM model • Valuation of defaultable callable bonds ValuationofDefaultable Bonds D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

33. Content • Chapter 3: Pricing Bond andCredit Derivatives • Pricing a credit-spreadputoption D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

34. Pricing a credit-spreadputoption Pricing Bond andCredit Derivatives D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

35. Pricing a credit-spreadputoption Pricing Bond andCredit Derivatives D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

36. Pricing a credit-spreadputoption Pricing Bond andCredit Derivatives D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

37. Pricing a credit-spreadputoption Pricing Bond andCredit Derivatives D.DuffieandK.J.Singleton, Modeling Term Structuresofdefaultable Bonds

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