利率衍生物定价的有效方法

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