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Recovery of Market Value

Andreas Gerwinski

Seminar Credit RiskDr. Frank SeifriedTU Kaiserslautern

17.Januar 2011

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

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

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

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

Valuation of defaultable Claims

Valuation equation or general pricing relation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

Pricing Bond and Credit Derivatives Pricing a credit-spread put option

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

Pricing Bond and Credit Derivatives Pricing a credit-spread put option

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

Pricing Bond and Credit Derivatives Pricing a credit-spread put option

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

Pricing Bond and Credit Derivatives Pricing a credit-spread put option

Thank you for your attention!