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

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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

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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

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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

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

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

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

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

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Thank you for your attention! 38

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