### Valuation of Defaultable Bonds

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Recovery of Market Value
Andreas Gerwinski
Seminar Credit Risk
Dr. Frank Seifried
TU Kaiserslautern
17.Januar 2011
2
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
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
3
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
4
Valuation of defaultable Claims
Valuation equation or general pricing relation
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
25
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
26
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
27
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
28
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
29
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
30
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
31
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
32
33
Content
Chapter 3: Pricing Bond and Credit Derivatives
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
Pricing Bond and Credit Derivatives
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
34
Pricing Bond and Credit Derivatives
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
35
Pricing Bond and Credit Derivatives