Valuation of Defaultable Bonds

Report
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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
Pricing a credit-spread put option
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
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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
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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
34
Pricing Bond and Credit Derivatives
Pricing a credit-spread put option
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
35
Pricing Bond and Credit Derivatives
Pricing a credit-spread put option
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
36
Pricing Bond and Credit Derivatives
Pricing a credit-spread put option
D.Duffie and K.J.Singleton, Modeling Term Structures of defaultable Bonds
37
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Thank you for your attention!

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