利率衍生物价值的有效计算方法

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 numeraire theorem 2.1.4 girsanov's theorem and ito's lemma 2.1.5 application： black-scholes model 2.1.6 application： foreign-exchange options 2.2 numerical methods 2.2.1 derivation of black-scholes partial differential equation 2.2.2 feynman-kac formula 2.2.3 numerical solution of pde's 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-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 formulae 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 gaussian model 6.1 spot rate process 6.1.1 partial differential equation 6.2 analytical formulee 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 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 measure 8.2.4 ti-forward measure 8.3 monte carlo simulation for libor market models 8.3.1 calculating the numeraire rebased payoff 8.3.2 example： vanilla cap 8.3.3 discrete 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 ti-forward measure 8.4.3 example： spread option 9. markov-functional 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 libor example： barrier caps 9.6.1 numerical calculation 9.6.2 comparison with libor market model 9.6.3 impact of mean-reversion 9.7 libor example： chooser- and auto-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 between models 10. an empirical comparison of market models 10.1 data description 10.2 libor market model 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 estimation and pricing results 10.4 conclusion 11. convexity correction 11.1 convexity correction and change of numeraire 11.1.1 multi-currency change of numeraire theorem 11.1.2 convexity correction 11.2 options on convexity corrected rates 11.2.1 option price formula 11.2.2 digital price formula 11.3 single index products 11.3.1 libor in arrears 11.3.2 constant maturity swap 11.3.3 diffed libor 11.3.4 diffed cms 11.4 multi-index products 11.4.1 rate based spread options 11.4.2 spread digital 11.4.3 other multi-index products 11.4.4 comparison with 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-factor models 12.3 volatility skews references index

《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。《利率衍生物定价的有效方法》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。