本書是一部全面講述計(jì)算和管理利率衍生物模型的教程。分為兩個部分:第一部分比較和討論了傳統(tǒng)模型,比如即期和遠(yuǎn)期利率模型;第二部分主要講述最新發(fā)展起來的市場模型。本書和同時期眾多圖書的不同之處在于,不僅專注于數(shù)學(xué)知識,并大量刻畫了作者在工業(yè)應(yīng)用中的實(shí)踐經(jīng)驗(yàn)。
目次:導(dǎo)引;套匯、鞅和數(shù)值方法;(一)即期和遠(yuǎn)期利率模型:即期和遠(yuǎn)期利率模型;基礎(chǔ)解和遠(yuǎn)期風(fēng)險調(diào)節(jié)策略;Hull-White模型;平方高斯模型;單因子模型的經(jīng)驗(yàn)比較;(二)市場利率模型:LIBOR和調(diào)劑市場模型;馬爾科夫函數(shù)模型;市場模型的經(jīng)驗(yàn)比較;凸性錯誤;擴(kuò)展和深究。
讀者對象:數(shù)學(xué)金融、經(jīng)濟(jì)專業(yè)的本科生、研究生和相關(guān)的從業(yè)人員。
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: 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
……
Part Ⅱ. Market Rate Models
References
Index