Springer Finance

Methods, Models, and Applications

By: Manuel Ammann

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Hardcover | 25 February 2002 | Edition Number 2

At a Glance

Hardcover
268 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 16.51 x 1.91

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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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You Can Find This Book In

Non-Fiction Business & Management Management & Management Techniques Management Decision Making Accounting & Finance Finance Investment & Securities Accounting Credit & Credit Institutions Banking Economics

Introduction	p. 1
Motivation	p. 1
Counterparty Default Risk	p. 2
Derivatives on Defaultable Assets	p. 6
Credit Derivatives	p. 7
Objectives	p. 8
Structure	p. 10
Contingent Claim Valuation	p. 13
Valuation in Discrete Time	p. 14
Definitions	p. 14
The Finite Setting	p. 15
Extensions	p. 18
Valuation in Continuous Time	p. 18
Definitions	p. 19
Arbitrage Pricing	p. 20
Fundamental Asset Pricing Theorem	p. 25
Applications in Continuous Time	p. 25
Black-Scholes Model	p. 26
Margrabe's Model	p. 30
Heath-Jarrow-Morton Framework	p. 33
Forward Measure	p. 38
Applications in Discrete Time	p. 41
Geometric Brownian Motion	p. 41
Heath-Jarrow-Morton Forward Rates	p. 43
Summary	p. 45
Credit Risk Models	p. 47
Pricing Credit-Risky Bonds	p. 47
Traditional Methods	p. 48
Firm Value Models	p. 48
Merton's Model	p. 48
Extensions and Applications of Merton's Model	p. 51
Bankruptcy Costs and Endogenous Default	p. 52
First Passage Time Models	p. 53
Intensity Models	p. 58
Jarrow-Turnbull Model	p. 58
Jarrow-Lando-Turnbull Model	p. 62
Other Intensity Models	p. 65
Pricing Derivatives with Counterparty Risk	p. 66
Firm Value Models	p. 66
Intensity Models	p. 67
Swaps	p. 68
Pricing Credit Derivatives	p. 70
Debt Insurance	p. 70
Spread Derivatives	p. 71
Empirical Evidence	p. 73
Summary	p. 74
A Firm Value Pricing Model for Derivatives with Counter-party Default Risk	p. 77
The Credit Risk Model	p. 77
Deterministic Liabilities	p. 79
Prices for Vulnerable Options	p. 80
Special Cases	p. 82
Fixed Recovery Rate	p. 83
Deterministic Claims	p. 84
Stochastic Liabilities	p. 85
Prices of Vulnerable Options	p. 87
Special Cases	p. 88
Asset Claims	p. 89
Debt Claims	p. 89
Gaussian Interest Rates and Deterministic Liabilities	p. 90
Forward Measure	p. 91
Prices of Vulnerable Stock Options	p. 93
Prices of Vulnerable Bond Options	p. 95
Special Cases	p. 95
Gaussian Interest Rates and Stochastic Liabilities	p. 96
Prices of Vulnerable Stock Options	p. 97
Prices of Vulnerable Bond Options	p. 99
Special Cases	p. 99
Vulnerable Forward Contracts	p. 99
Numerical Examples	p. 100
Deterministic Interest Rates	p. 100
Stochastic Interest Rates	p. 103
Forward Contracts	p. 110
Summary	p. 113
Proofs of Propositions	p. 115
Proof of Proposition 4.2.1	p. 115
Proof of Proposition 4.3.1	p. 120
Proof of Proposition 4.4.1	p. 125
Proof of Proposition 4.5.1	p. 132
A Hybrid Pricing Model for Contingent Claims with Credit Risk	p. 141
The General Credit Risk Framework	p. 141
Independence and Constant Parameters	p. 143
Price Reduction and Bond Prices	p. 145
Model Specifications	p. 146
Arrival Rate of Default	p. 146
Recovery Rate	p. 147
Bankruptcy Costs	p. 148
Implementations	p. 149
Lattice with Deterministic Interest Rates	p. 149
The Bankruptcy Process	p. 153
An Extended Lattice Model	p. 155
Stochastic Interest Rates	p. 157
Recombining Lattice versus Binary Tree	p. 158
Prices of Vulnerable Options	p. 159
Recovering Observed Term Structures	p. 160
Recovering the Risk-Free Term Structure	p. 160
Recovering the Defaultable Term Structure	p. 161
Default-Free Options on Risky Bonds	p. 162
Put-Call Parity	p. 163
Numerical Examples	p. 164
Deterministic Interest Rates	p. 164
Stochastic Interest Rates	p. 168
Computational Cost	p. 171
Summary	p. 173
Pricing Credit Derivatives	p. 175
Credit Derivative Instruments	p. 176
Credit Derivatives of the First Type	p. 176
Credit Derivatives of the Second Type	p. 178
Other Credit Derivatives	p. 178
Valuation of Credit Derivatives	p. 178
Payoff Functions	p. 180
Credit Forward Contracts	p. 180
Credit Spread Options	p. 182
The Compound Pricing Approach	p. 183
Firm Value Model	p. 183
Stochastic Interest Rates	p. 187
Intensity and Hybird Credit Risk Models	p. 188
Numerical Examples	p. 189
Deterministic Interest Rates	p. 189
Stochastic Interest Rates	p. 193
Pricing Spread Derivatives with a Reduced-Form Model	p. 194
Credit Derivatives as Exchange Options	p. 198
Process Specifications	p. 198
Price of an Exchange Option	p. 200
Credit Derivatives with Counterparty Default Risk	p. 205
Price of an Exchange Option with Counterparty Default Risk	p. 205
Summary	p. 215
Conclusion	p. 217
Summary	p. 218
Practical Implications	p. 220
Future Research	p. 220
Useful Tools from Martingale Theory	p. 223
Probabilistic Foundations	p. 223
Process Classes	p. 225
Martingales	p. 225
Brownian Motion	p. 227
Stochastic Integration	p. 229
Change of Measure	p. 233
References	p. 237
List of Figures	p. 247
List of Tables	p. 249
Index	p. 251
Table of Contents provided by Syndetics. All Rights Reserved.

Springer Finance

Methods, Models, and Applications

At a Glance

Hardcover

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