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