1. Recovery of Market Value Andreas Gerwinski Seminar Credit Risk Dr. Frank Seifried TU Kaiserslautern 17.Januar 2011 1

2. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Content Chapter 1: Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate Chapter 2: Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds Chapter 3: Pricing Bond and Credit Derivatives Pricing a credit-spread put option 2

3. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Content Chapter 1: Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 3

4. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable 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 4

5. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims Valuation equation or general pricing relation 5

6. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 6

7. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 7

8. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 8

9. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 9

10. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 10

11. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 11

12. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 12

13. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 13

14. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 14

15. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of defaultable Claims a discrete-time Motivation Continuous-time valuation Exogenous expected loss rate a continuous-time Markov formulation Price dependent expected loss rate 15

16. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Content Chapter 2: Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 16

17. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 17

18. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 18

19. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 19

20. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 20

21. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 21

22. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 22

23. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 23

24. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 24

25. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 25

26. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 26

27. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 27

28. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 28

29. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 29

30. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 30

31. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 31

32. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Valuation of Defaultable Bonds Recovery and valuation of bonds Valuation of noncallable corporate bonds a defaultable HJM model Valuation of defaultable callable bonds 32

33. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Content Chapter 3: Pricing Bond and Credit Derivatives Pricing a credit-spread put option 33

34. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Pricing Bond and Credit Derivatives Pricing a credit-spread put option 34

35. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Pricing Bond and Credit Derivatives Pricing a credit-spread put option 35

36. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Pricing Bond and Credit Derivatives Pricing a credit-spread put option 36

37. D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds Pricing Bond and Credit Derivatives Pricing a credit-spread put option 37

38. Thank you for your attention! 38