利率衍生物定價的有效方法(英文) | 被動收入的投資秘訣 - 2024年11月
利率衍生物定價的有效方法(英文)
是一部全面講述計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模型,比如即期和遠期利率模型;第二部分主要講述最新發展起來的市場模型。全書和同時期眾多圖書的不同之處在於,不僅專注於數學知識,並大量刻畫了作者在工業應用中的實踐經驗。
1. Introduction2. Arbitrage, Martingales and Numerical Methods2.1 Arbitrage and Martingales2.1.1 Basic Setup2.1.2 Equivalent Martingale Measure2.1.3 Change of Numeraire Theorem2.1.4 Girsanov’’s Theorem and It6’’s Lemma2.1.5 Application: Black-Scholes Model2.1.6 Application: Foreign-Exchange Options2.2 Numerical Methods2.2.1 Derivation of Black-Scholes Partial Differential Equation2.2.2 Feynman-Kac Formula2.2.3 Numerical Solution of PDE’’s2.2.4 Monte Carlo Simulation2.2.5 Numerical IntegrationPart Ⅰ. Spot and Forward Rate Models3. Spot and Forward Rate Models3.1 Vasicek Methodology3.1.1 Spot Interest Rate3.1.2 Partial Differential Equation3.1.3 Calculating Prices3.1.4 Example: Ho-Lee Model3.2 Heath-Jarrow-Morton Methodology3.2.1 Forward Rates3.2.2 Equivalent Martingale Measure3.2.3 Calculating Prices3.2.4 Example: Ho-Lee Model3.3 Equivalence of the Methodologies4. Fundamental Solutions and the Forward-Risk-Adjusted Measure4.1 Forward-Risk-Adjusted Measure4.2 Fundamental Solutions4.3 Obtaining Fundamental Solutions4.4 Example: Ho-Lee Model4.4.1 Radon-Nikodym Derivative4.4.2 Fundamental Solutions4.5 Fundamental Solutions for Normal Models5. The Hull-White Model5.1 Spot Rate Process5.1.1 Partial Differential Equation5.1.2 Transformation of Variables5.2 Analytical Formulae5.2.1 Fundamental Solutions5.2.2 Option Prices5.2.3 Prices for Other Instruments5.3 Implementation of the Model5.3.1 Fitting the Model to the Initial Term-Structure5.3.2 Transformation of Variables5.3.3 Trinomial Tree5.4 Performance of the Algorithm5.5 Appendix……Part Ⅱ. Market Rate ModelsReferencesIndex