佩尔森著的《利率衍生物定价的有效方法》是一部全面讲述计算和管理利率衍生物模型的教程。分为两个部分：第一部分比较和讨论了传统模型，比如即期和远期利率模型；第二部分主要讲述最新发展起来的市场模型。本书和同时期众多图书的不同之处在于，不仅专注于数学知识，并大量刻画了作者在工业应用中的实践经验。目次：导引；套汇、鞅和数值方法；（一）即期和远期利率模型：即期和远期利率模型；基础解和远期风险调节策略；Hull—White模型；平方高斯模型；单因子模型的经验比较；（二）市场利率模型：LIBOR和调剂市场模型；马尔科夫函数模型；市场模型的经。

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 Numeralre Theorem

2.1.4 Girsanov'S Theorem and Ito'S Lemma

2.1.5 Application：Black.Scholes Model

2.1.6 Application：Foreign-ExchangeOptions

2.2 Numerical Metbods

2.2.1 Derivation of Black-Scboles Partial Differential

 Equation

2.2.2 Feynman-Kac Formula

2.2.3 Numerical Solution of PDE'

2.2.4 Monte Carlo Simulation

2.2.5 Numerical Integration

Part 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-LeeModel

3.3 E quivalence 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. TheHull-White Model

5.1 Spot Rate Process

5.1.1 Partial Difierential Equation

5.1.2 Transformation of Variables

5.2 Analytical Formulae

5.2.1 Fundamental Solutions

5.2.2 OptionPrices

5.2.3 Pricesfor Other Instruments

5.3 Implementation oftheModel

5.3.1 Fitting the Model to the Initial Term-Structure

5.3.2 Transformation ofVariables

5.3.3 Trinomial Tree

5.4 Performance ofthe Algorithm.

5.5 Appendix

6. The Squared Gatmsian Model

6.1 Spot Rate Process

6.1.1PartialDifferential Equation

6.2 AnaIytical Formulm

6.2.1 Fundarnental 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 ninomial Tree

6.4 Appendix A

6.5 Appendix B

7. An Empirical Comparison of 0ne-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 Models

8. LIBOR and Swap Market Models

8.1 LIBOR Market Models

8.1.1 LIBOR Process

8.1.2 Caplet Price

8.1.3 Terminal Measure

8.2 Swap Market Models

8.2.1 Interest Rate Swaps

8.2.2 Swaption Price

8.2.3 Terminal Mcaste

8.2.4 T1-Forward Measure………

8.3 Monte Carlo Simulation for LIBOR Market Models

8.3.1 Calculating the Numeralre Rebased Payoff

8.3.2 Example：Vanilla Cap

8.3.3 Diserete Barrier Caps／Floors

8.3.4 Discrete Barrier Digital Caps/Floors

8.3.5 Payment Stream

8.3.6 Ratchets

8.4 Monte Carlo Simulation for Swap Market Models

8.4.1 Terminal Measure

8.4.2 T1-Forward Measure

8.4.3 Example：Spread Option

9. Markov-Funetional Models

9.1 Basic Assumptions

9.2 LIBOR Markov-Functional Model

9.3 Swap Markov-Functional Model

9.4 Numerical Implementation

9.4.1 Numerical Integration

9.4.2 Non-Parametric Implementation

9.4.3 Semi-Parametric Implementation

9.5 Forward Volatilities and Auto-Correlation

9.5.1 Mean-Reversion and Auto-Correlation

9.5.2 Auto-Correlation and the Volatility Function

9.6 IBOR Example:Barries Caps

9.6.1 Numefical CaIculation

9.6.2 Comparison with LIBOR Market Model

9.6.3 Impact of Mean-Reversion

9.7 LIBOR Example：Chooser-andAuto-Caps

9.7.1 Auto-Caps／Floors

9.7.2 Chooser-Caps／Floors

9.7.3 Auto-and Chooser-Digitals

9.7.4 Numerical Implementation

9.8 Swap Example：Bermudan Swaptions

9.8.1 Early Notification

9.8.2 Comparison BetweenMoriels

10. An Empirical Comparison of Market Models

10.1 Data Description

10.2 LIBOR Market ModeI

10.2.1 Calibration Methodology

10.2.2 Estimation and Pricing Results

10.3 Swap Market Model

10.3.1 Calibration Methodology

10.3.2 Estimationand Pricing Resuits

10.4 Conclusion

11. Convexity Correction

11.1 Convexity Correction and Change of Numeraire

11.1.1 Multi-urrency Change of Numeraire Theorem

11.1.2 Convexity Correction

11.2 Options on Convexity Corrected Rares

11.2.1 Option Price Formula

11.2.2 Digital Price Formula

11.3 SingleIndex Products

11.3.1 LIBOR in Arrears

11.3.2 Constant Maturity Swap

1l.3.3 Diffed LIBOR

11.3.4 Diffed CMS

11.4 Multi-Index Products

11.4.1 Rate Based Spreadoptions

1l.4.2 Spread Digital

11.4.3 Other Multi-ndex Products

11.4.4 Comparisonwith Market Models

11.5 A Warning on Convexity Correction

11.6 Appendix：Linear Swap Rate Model

12. Extensions and Further Developments

12.1 General Philosophy

12.2 Multi-actor Models

12.3 V0latility Skews

References

Index