Pricing Interest-Rate Derivatives (eBook)

Foreword 6
Acknowledgements 7
Contents 8
List of Abbreviations and Symbols 11
List of Tables 14
List of Figures 16
1 Introduction 18
1.1 Motivation and Objectives 18
1.2 Structure of the Thesis 21
2 A General Multi-Factor Model of the Term Structure of Interest Rates and the Principles of Characteristic Functions 23
2.1 An Extended Jump-Diffusion Term-Structure Model 23
2.2 Technical Preliminaries 27
2.3 The Risk-Neutral Pricing Approach 29
2.4 The Characteristic Function 37
3 Theoretical Prices of European Interest-Rate Derivatives 47
3.1 Overview 47
3.2 Derivatives with Unconditional Payoff Functions 48
3.3 Derivatives with Conditional Payoff Functions 54
4 Three Fourier Transform-Based Pricing Approaches 61
4.1 Overview 61
4.2 Heston Approach 65
4.3 Carr-Madan Approach 71
4.4 Lewis Approach 76
5 Payoff Transformations and the Pricing of European Interest-Rate Derivatives 85
5.1 Overview 85
5.2 Unconditional Payoff Functions 86
5.3 Conditional Payoff Functions 97
6 Numerical Computation of Model Prices 110
6.1 Overview 110
6.2 Contracts with Unconditional Exercise Rights 111
6.3 Contracts with Conditional Exercise Rights 112
7 Jump Specifications for Afine Term-Structure Models 126
7.1 Overview 126
7.2 Exponentially Distributed Jumps 130
7.3 Normally Distributed Jumps 132
7.4 Gamma Distributed Jumps 135
8 Jump-Enhanced One-Factor Interest-Rate Models 139
8.1 Overview 139
8.2 The Ornstein-Uhlenbeck Model 140
8.3 The Square-Root Model 150
9 Jump-Enhanced Two-Factor Interest-Rate Models 158
9.1 Overview 158
9.2 The Additive OU-SR Model 159
9.3 The Fong-Vasicek Model 172
10 Non-Affine Term-Structure Models and Short-Rate Models with Stochastic Jump Intensity 184
10.1 Overview 184
10.2 Quadratic Gaussian Models 184
10.3 Stochastic Jump Intensity 187
11 Conclusion 188
A Derivation of the Complex-Valued Coefficients for the Characteristic Function in the Square-Root Model 192
B Derivation of the Complex-Valued Coe.cients for the Characteristic Function in the Fong-Vasicek Model 195
References 199