Bouziane Pricing Interest-Rate Derivatives

A Fourier-Transform Based Approach
1. Auflage 2008
ISBN: 978-3-540-77066-4
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 607, 193 Seiten

Reihe: Lecture Notes in Economics and Mathematical Systems

The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.

Autoren/Hrsg.

Bouziane, Markus

Inhaltsverzeichnis

1;Foreword;6
2;Acknowledgements;7
3;Contents;8
4;List of Abbreviations and Symbols;11
5;List of Tables;14
6;List of Figures;16
7;1 Introduction;18
7.1;1.1 Motivation and Objectives;18
7.2;1.2 Structure of the Thesis;21
8;2 A General Multi-Factor Model of the Term Structure of Interest Rates and the Principles of Characteristic Functions;23
8.1;2.1 An Extended Jump-Diffusion Term-Structure Model;23
8.2;2.2 Technical Preliminaries;27
8.3;2.3 The Risk-Neutral Pricing Approach;29
8.4;2.4 The Characteristic Function;37
9;3 Theoretical Prices of European Interest-Rate Derivatives;47
9.1;3.1 Overview;47
9.2;3.2 Derivatives with Unconditional Payoff Functions;48
9.3;3.3 Derivatives with Conditional Payoff Functions;54
10;4 Three Fourier Transform-Based Pricing Approaches;61
10.1;4.1 Overview;61
10.2;4.2 Heston Approach;65
10.3;4.3 Carr-Madan Approach;71
10.4;4.4 Lewis Approach;76
11;5 Payoff Transformations and the Pricing of European Interest-Rate Derivatives;85
11.1;5.1 Overview;85
11.2;5.2 Unconditional Payoff Functions;86
11.3;5.3 Conditional Payoff Functions;97
12;6 Numerical Computation of Model Prices;110
12.1;6.1 Overview;110
12.2;6.2 Contracts with Unconditional Exercise Rights;111
12.3;6.3 Contracts with Conditional Exercise Rights;112
13;7 Jump Specifications for Afine Term-Structure Models;126
13.1;7.1 Overview;126
13.2;7.2 Exponentially Distributed Jumps;130
13.3;7.3 Normally Distributed Jumps;132
13.4;7.4 Gamma Distributed Jumps;135
14;8 Jump-Enhanced One-Factor Interest-Rate Models;139
14.1;8.1 Overview;139
14.2;8.2 The Ornstein-Uhlenbeck Model;140
14.3;8.3 The Square-Root Model;150
15;9 Jump-Enhanced Two-Factor Interest-Rate Models;158
15.1;9.1 Overview;158
15.2;9.2 The Additive OU-SR Model;159
15.3;9.3 The Fong-Vasicek Model;172
16;10 Non-Affine Term-Structure Models and Short-Rate Models with Stochastic Jump Intensity;184
16.1;10.1 Overview;184
16.2;10.2 Quadratic Gaussian Models;184
16.3;10.3 Stochastic Jump Intensity;187
17;11 Conclusion;188
18;A Derivation of the Complex-Valued Coefficients for the Characteristic Function in the Square-Root Model;192
19;B Derivation of the Complex-Valued Coe.cients for the Characteristic Function in the Fong-Vasicek Model;195
20;References;199