Efficient methods for valuing interest rate derivatives评价利率衍生物的有效方法

2000-9  

Springer Verlag  

Pelsser, Antoon  

172  

无  

interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore the practical issues, such as the implementation of models, and model selection. Aimed at people with a solid quantitative background, this book will be of particular interest to risk managers, interest rate derivative traders, quantitative researchers, portfolio and fund managers, and students of mathematics and economics, but it will also prove invaluable to anyone looking for a good overview of interest rate derivative modelling.

　1. Introduction　2. Arbitrage, Martingales and Numerical Methods　　2.1 Arbitrage and Martingales　　　2.1.1 Basic Setup　　　2.1.2 Equivalent Martingale Measure　　　2.1.3 Change of Numeraire Theorem　　　2.1.4 Girsanov's Theorem and It6's Lemma　　　2.1.5 Application: B~ack-Scholes Model　　　2.1.6 Application: Foreign-Exchange Options　　2.2 Numerical Methods　　　2.2.1 Derivation of Black-Scholes Partial DifferentialEquation　　　2.2.2 Feynman-Kac Formula　　　2.2.3 Numerical Solution of PDE's　　　2.2.4 Monte Carlo Simulation　　　2.2.5 Numerical IntegrationPart Ⅰ Spot and Forward Rate Models　3. Spot and Forward Rate Models　　3.1 Vasicek Methodology　　　 3.1.1 Spot Interest Rate　　　 3.1.2 Partial Differential Equation　　　 3.1.3 Calculating Prices　　　 3.1.4 Example: Ho-Lee Model　　 3.2 Heath-Jarrow-Morton Methodology　　　 3.2.1 Forward Rates　　　 3.2.2 Equivalent Martingale Measure　　　 3.2.3 Calculating Prices　　　 3.2.4 Example: Ho-Lee Model　　 3.3 Equivalence of the Methodologies　4. Fundamental Solutions and the Forward-Risk-Adjusted Measure　　4.1 Forward-Risk-Adjusted Measure　　4.2 Fundamental Solutions　　4.3 Obtaining Fundamental Solutions　　4.4 Example: Ho-Lee Model　　　4.4.1 Radon-Nikodym Derivative　　　4.4.2 Fundamental Solutions　　4.5 Fundamental Solutions for Normal Models 5. The Hull-White Model　　5.1 Spot Rate Process　　　5.1.1 Partial Differential Equation　　　5.1.2 Transformation of Variables　　5.2 Analytical Formul2e　　　5.2.1 Fundamental Solutions　　　5.2.2 Option Prices　　　5.2.3 Prices for Other Instruments　　5.3 Implementation of the Model　　　5.3.1 Fitting the Model to the Initial Term-Structure 　　　5.3.2 Transformation of Variables　　　5.3.3 Trinomial Tree　　5.4 Performance of the Algorithm　　5.5 Appendix 6. The Squared Gatmsian Model　　6.1 Spot Rate Process　　　6.1.1 Partial Differential Equation　　6.2 Analytical Formulae　　　6.2.1 Fundamental Solutions　　　6.2.2 Option Prices　　6.3 Implementation of the Model　　　6.3.1 Fitting the Model to the Initial Term-Structure 　　　6.3.2 Trinomial Tree　　6.4 Appendix A　　6.5 Appendix B 7. An Empirical Comparison of One-Factor Models　　7.1 Yield-Curve Models　　7.2 Econometric Approach　　7.3 Data　　7.4 Empirical Results　　7.5 Conclusions ……Part Ⅱ Market Rate ModelsReferencesIndex

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