Credit Risk Valuation: Methods, Models, and Applications

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Springer Science & Business Media, Feb 25, 2002 - Business & Economics - 255 pages
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Credit risk is an important consideration in most financial transactions. As for any other risk, the risk taker requires compensation for the undiversifiable part of the risk taken. In bond markets, for example, riskier issues have to promise a higher yield to attract investors. But how much higher a yield? Using methods from contingent claims analysis, credit risk valuation models attempt to put a price on credit risk. This monograph gives an overview of the current methods for the valu ation of credit risk and considers several applications of credit risk models in the context of derivative pricing. In particular, credit risk models are in corporated into the pricing of derivative contracts that are subject to credit risk. Credit risk can affect prices of derivatives in a variety of ways. First, financial derivatives can be subject to counterparty default risk. Second, a derivative can be written on a security which is subject to credit risk, such as a corporate bond. Third, the credit risk itself can be the underlying vari able of a derivative instrument. In this case, the instrument is called a credit derivative. Fourth, credit derivatives may themselves be exposed to counter party risk. This text addresses all of those valuation problems but focuses on counterparty risk. The book is divided into six chapters and an appendix. Chapter 1 gives a brief introduction into credit risk and motivates the use of credit risk models in contingent claims pricing.
 

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Contents

Introduction
1
12 Objectives
8
13 Structure
10
Contingent Claim Valuation
13
21 Valuation in Discrete Time
14
22 Valuation in Continuous Time
18
23 Applications in Continuous Time
25
24 Applications in Discrete Time
41
54 Recovering Observed Term Structures
158
55 DefaultFree Options on Risky Bonds
160
56 Numerical Examples
162
57 Computational Cost
169
58 Summary
171
Pricing Credit Derivatives
173
61 Credit Derivative Instruments
174
62 Valuation of Credit Derivatives
176

25 Summary
45
Credit Risk Models
47
32 Pricing Derivatives with Counterparty Risk
66
33 Pricing Credit Derivatives
70
34 Empirical Evidence
73
35 Summary
74
A Firm Value Pricing Model for Derivatives with Counterparty Default Risk
77
42 Deterministic Liabilities
79
43 Stochastic Liabilities
85
44 Gaussian Interest Rates and Deterministic Liabilities
90
45 Gaussian Interest Rates and Stochastic Liabilities
96
46 Vulnerable Forward Contracts
99
47 Numerical Examples
100
48 Summary
113
49 Proofs of Propositions
115
A Hybrid Pricing Model for Contingent Claims with Credit Risk
139
52 Implementations
147
53 Prices of Vulnerable Options
157
63 The Compound Pricing Approach
181
64 Numerical Examples
187
65 Pricing Spread Derivatives with a ReducedForm Model
192
66 Credit Derivatives as Exchange Options
196
67 Credit Derivatives with Counterparty Default Risk
203
68 Summary
213
Conclusion
215
71 Summary
216
72 Practical Implications
218
Useful Tools from Martingale Theory
221
A2 Process Classes
223
A4 Brownian Motion
225
A5 Stochastic Integration
227
A6 Change of Measure
231
References
235
List of Tables
245
Index
247
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