内容提要 本书英文版是剑桥出版社的“数学、金融与风险”(Mathematics, Finance and Risk)系列中的一本,其由高等教育出版社影印出版发行。 与大多数有关投资学、金融工程或衍生证券的书不同的是,本书从金融学的基本观念出发,逐步构建理论。在现代金融学中所需要的高级数学概念以一种可接受的层次来阐释。这样,它就为金融方面的MBA、有志于从事金融业的理工科学生、计算金融的研究工作者、系统分析师和金融工程师在这一主题上提供了全面的基础。 构建理论的同时,作者介绍在定价、风险管理和证券组合管理方面的计算技巧的算法,并且对它们的效率进行了分析。对金融证券和衍生证券的定价是本书的中心论题。各种各样的金融工具都得到讨论:债券、期权、期货、远期、利率衍生品、有抵押支持的证券、嵌入期权的债券,以及诸如此类的其他工具。为便于参考使用,每种金融工具都以简短而自成体系的一章来论述。 本书可供金融MBA、金融学和金融工程方向的学生、计算金融的研究人员以及金融分析师参考使用。 目录 PrefaceUseful Abbreviations1 Introduction1.1 Modern Finance: A Brief History1.2 Financial Engineering and Computation1.3 Financial Markets1.4 Computer Technology2 Analysis of Algorithms2.1 Complexity2.2 Analysis of Algorithms2.3 Description of Algorithms2.4 Software Implementation3 Basic Financial Mathematics3.1 Time Value of Money3.2 Annuities3.3 Amortization3.4 Yields3.5 Bonds4 Bond Price Volatility4.1 Price Volatility4.2 Duration4.3 Convexity5 Term Structure of Interest Rates5.1 Introduction5.2 Spot Rates5.3 Extracting Spot Rates from Yield Curves5.4 Static Spread5.5 Spot Rate Curve and Yield Curve5.6 Forward Rates5.7 Term Structure Theories5.8 Duration and Immunization Revisited6 Fundamental Statistical Concepts6.1 Basics6.2 Regression6.3 Correlation6.4 Parameter Estimation7 Option Basics7.1 Introduction7.2 Basics7.3 Exchange-Traded Options7.4 Basic Option Strategies8 Arbitrage in Option Pricing8.1 The Arbitrage Argument8.2 Relative Option Prices8.3 Put-Call Parity and Its Consequences8.4 Early Exercise of American Options8.5 Convexity of Option Prices8.6 The Option Portfolio Property9 Option Pricing Models9.1 Introduction9.2 The Binomial Option Pricing Model9.3 The Black-Scholes Formula9.4 Using the Black-Scholes Formula9.5 American Puts on a Non-Dividend-Paying Stock9.6 Options on a Stock that Pays Dividends9.7 Traversing the Tree Diagonally10 Sensitivity Analysis of Options10.1 Sensitivity Measures ("The Greeks")10.2 Numerical Techniques11 Extensions of Options Theory11.1 Corporate Securities11.2 Barrier Options11.3 Interest Rate Caps and Floors11.4 Stock Index Options11.5 Foreign Exchange Options11.6 Compound Options11.7 Path-Dependent Derivatives12 Forwards, Futures, Futures Options, Swaps12.1 Introduction12.2 Forward Contracts12.3 Futures Contracts12.4 Futures Options and Forward Options12.5 Swaps13 Stochastic Processes and Brownian Motion13.1 Stochastic Processes13.2 Martingales ("Fair Games")13.3 Brownian Motion13,4 Brownian Bridge14 Continuous-Time Financial Mathematics14.1 Stochastic Integrals14.2 Ito Processes14.3 Applications14.4 Financial Applications15 Continuous-Time Derivatives Pricing15.1 Partial Differential Equations15.2 The Black-Schotes Differential Equation15.3 Applications15.4 General Derivatives Pricing15.5 Stochastic Volatility16 Hedging16.1 Introduction16.2 Hedging and Futures16.3 Hedging and Options17 Trees17.1 Pricing Barrier Options with Combinatorial Methods17.2 Trinomial Tree Algorithms17.3 Pricing Multivariate Contingent Claims18 Numerical Methods18.1 Finite-Difference Methods18.2 Monte Carlo Simulation18.3 Quasi-Monte Carlo Methods19 Matrix Computation19.1 Fundamental Definitions and Results19.2 Least-Squares Problems19.3 Curve Fitting with Splines20 Time Series Analysis20.1 Introduction20.2 Conditional Variance Models for Price Volatility21 Interest Rate Derivative Securities21.1 Interest Rate Futures and Forwards21.2 Fixed-Income Options and Interest Rate Options21.3 Options on Interest Rate Futures21.4 Interest Rate Swaps22 Term Structure Fitting22.1 Introduction22.2 Linear Interpolation22.3 Ordinary Least Squares22.4 Splines22.5 The Nelson-Siegel Scheme23 Introduction to Term Structure Modeling23.1 Introduction23.2 The Binomial Interest Rate Tree23.3 Applications in Pricing and Hedging23.4 Volatility Term Structures24 Foundations of Term Structure Modeling24.1 Terminology24.2 Basic Relations24.3 Risk-Neutral Pricing24.4 The Term Structure Equation24.5 Forward-Rate Process24.6 The Binomial Model with Applications24.7 Black-Scholes Models25 Equilibrium Term Structure Models25.1 The Vasicek Model25.2 The Cox-Ingersoll-Ross Model25.3 Miscellaneous Models25.4 Model Calibration25.5 One-Factor Short Rate Models26 No-Arbitrage Term Structure Models26.1 Introduction26.2 The Ho-Lee Model26.3 The Black-Derman-Toy Model26.4 The Models According to Hull and White26.5 The Heath-Jarrow-Morton Model26.6 The Ritchken-Sankarasubramanian Model27 Fixed-Income Securities27.1 Introduction27.2 Treasury, Agency, and Municipal Bonds27.3 Corporate Bonds27.4 Valuation Methodologies27.5 Key Rate Durations28 Introduction to Mortgage-Backed Securities28.1 Introduction28.2 Mortgage Banking28.3 Agencies and Securitization28.4 Mortgage-Backed Securities28.5 Federal Agency Mortgage-Backed Securities Programs28.6 Prepayments29 Analysis of Mortgage-Backed Securities29.1 Cash Flow Analysis29.2 Collateral Prepayment Modeling29.3 Duration and Convexity29.4 Valuation Methodologies30 Collateralized Mortgage Obligations30.1 Introduction30.2 Floating-Rate Tranches30.3 PAC Bonds30.4 TAC Bonds30.5 CMO Strips30.6 Residuals31 Modern Portfolio Theory31.1 Mean-Variance Analysis of Risk and Return31.2 The Capital Asset Pricing Model31.3 Factor Models31.4 Value at Risk32 Software32.1 Web Programming32.2 Use of The Capitals Software32.3 Further Topics33 Answers to Selected ExercisesBibliographyGlossary of Useful NotationsIndex 作者介绍
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