金融衍生品数学模型

出版时间：2010-4  出版社：世界图书出版公司  作者：郭宇权  页数：530  
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前言

In the past three decades, we have witnessed the phenomenal growth in the trading of financial derivatives and structured products in the financial markets around the globe and the surge in research on derivative pricing theory,cading financial institutions are hiring graduates with a science background who can use advanced analyrical and numerical techniques to price financial derivatives and manage portfolio risks, a phenomenon coined as Rocket Science on Wall Street. There are now more than a hundred Master level degreed programs in Financial Engineering/Quantitative Finance/Computational Finance in different continents. This book is written as an introductory textbook on derivative pricing theory for students enrolled in these degree programs. Another audience of the book may include practitioners in quantitative teams in financial institutions who would like to acquire the knowledge of option pricing techniques and explore the new development in pricing models of exotic structured derivatives. The level of mathematics in this book is tailored to readers with preparation at the advanced undergraduate level of science and engineering majors, in particular, basic proficiencies in probability and statistics, differential equations, numerical methods, and mathematical analysis. Advance knowledge in stochastic processes that are relevant to the martingale pricing theory, like stochastic differential calculus and theory of martingale, are introduced in this book.The cornerstones of derivative pricing theory are the Black-Scholes-Merton pricing model and the martingale pricing theory of financial derivatives. The renowned risk neutral valuation principle states that the price of a derivative is given by the expectation of the discounted terminal payoff under the risk neutral measure,in accordance with the property that discounted security prices are martingales under this measure in the financial world of absence of arbitrage opportunities. This second edition presents a substantial revision of the first edition. The new edition presents the theory behind modeling derivatives, with a strong focus on the martingale pricing principle. The continuous time martingale pricing theory is motivated through the analysis of the underlying financial economics principles within a discrete time framework. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analyzed, emphasizing on the aspects of pricing, hedging, and their risk management. Starting from the Black-Scholes-Merton formulation of the option pricing model, readers are guided through the book on the new advances in the state-of-the-art derivative pricing models and interest rate models. Both analytic techniques and numerical methods for solving various types of derivative pricing models are emphasized. A large collection of closed form price formulas of various exotic path dependent equity options （like barrier options, lookback options, Asian options, and American options） and fixed income derivatives are documented.

内容概要

本书旨在运用金融工程方法讲述模型衍生品背后的理论，作为重点介绍了对大多数衍生证券很常用的鞅定价原理。书中还分析了固定收入市场中的大量金融衍生品，强调了定价、对冲及其风险策略。本书从著名的期权定价模型的Black-Scholes-Merton公式开始，讲述衍生品定价模型和利率模型中的最新进展，解决各种形式衍生品定价问题的解析技巧和数值方法。目次：衍生品工具介绍；金融经济和随机计算；期权定价模型；路径依赖期权；美国期权；定价期权的数值方案；利率模型和债券计价；利率衍生品：债券期权、LIBOR和交换产品。

书籍目录

Preface 1 Introduction to Derivative Instruments 　1.1Financial Options and Their Trading Strategies 　　1.1.1Trading Strategies Involving Options 　1.2Rational Boundaries for Option Values 　　1.2.1Effects of Dividend Payments 　　1.2.2Put-Call Parity Relations 　　1.2.3Foreign Currency Options 　1.3Forward and Futures Contracts 　　1.3.1Values and Prices of Forward Contracts 　　1.3.2Relation between Forward and Futures Prices 　1.4Swap Contracts 　　1.4.1Interest Rate Swaps 　　1.4.2Currency Swaps 　1.5Problems 2 Financial Economics and Stochastic Calculus 　2.1Single Period Securities Models 　　2.1.1Dominant Trading Strategies and Linear Pricing Measures 　　2.1.2Arbitrage Opportunities and Risk Neutral Probability Measures 　　2.1.3Valuation of Contingent Claims 　　2.1.4Principles of Binomial Option Pricing Model 　2.2Filtrations, Martingales and Multiperiod Models 　　2.2.1Information Structures and Filtrations 　　2.2.2Conditional Expectations and Martingales 　　2.2.3Stopping Times and Stopped Processes 　　2.2.4Multiperiod Securities Models 　　2.2.5Multiperiod Binomial Models 　2.3Asset Price Dynamics and Stochastic Processes 　　2.3.1Random Walk Models 　　2.3.2Brownian Processes 　2.4Stochastic Calculus: Ito's Lemma and Girsanov's Theorem 　　2.4.1Stochastic Integrals 　　2.4.2Ito's Lemma and Stochastic Differentials 　　2.4.3Ito's Processes and Feynman-Kac Representation Formula 　　2.4.4Change of Measure: Radon-Nikodym Derivative and Girsanov's Theorem. 　2.5Problems 3 Option Pricing Models: Blaek-Scholes-Merton Formulation 　3.1Black-Scholes-Merton Formulation 　　3.1.1Riskless Hedging Principle 　　3.1.2Dynamic Replication Strategy 　　3.1.3Risk Neutrality Argument 　3.2Martingale Pricing Theory 　　3.2.1Equivalent Martingale Measure and Risk Neutral Valuation 　　3.2.2Black-Scholes Model Revisited 　　3.3Black-Scholes Pricing Formulas and Their Properties 　3.3.1Pricing Formulas for European Options 　　3.3.2Comparative Statics 　3.4Extended Option Pricing Models 　　3.4.1Options on a Dividend-Paying Asset 　　3.4.2Futures Options 　　3.4.3Chooser Options 　　3.4.4Compound Options 　　3.4.5Merton's Model of Risky Debts 　　3.4.6Exchange Options 　　3.4.7Equity Options with Exchange Rate Risk Exposure 　3.5Beyond the Black-Scholes Pricing Framework 　　3.5.1Transaction Costs Models 　　3.5.2Jump-Diffusion Models 　　3.5.3Implied and Local Volatilities 　　3.5.4Stochastic Volatility Models 　3.6Problems 4 Path Dependent Options 　4.1Barrier Options 　　4.1.1European Down-and-Out Call Options 　　4.1.2Transition Density Function and First Passage Time Density 　　4.1.3Options with Double Barriers 　　4.1.4Discretely Monitored Barrier Options 　4.2Lookback Options 　　4.2.1European Fixed Strike Lookback Options 　　4.2.2European Floating Strike Lookback Options 　　4.2.3More Exotic Forms of European Lookback Options 　　4.2.4Differential Equation Formulation 　　4.2.5Discretely Monitored Lookback Options 　4.3Asian Options. 　　4.3.1Partial Differential Equation Formulation 　　4.3.2Continuously Monitored Geometric Averaging Options 　　4.3.3Continuously Monitored Arithmetic Averaging Options 　　4.3.4Put-Call Parity and Fixed-Floating Symmetry Relations 　　4.3.5Fixed Strike Options with Discrete Geometric Averaging 　　4.3.6Fixed Strike Options with Discrete Arithmetic Averaging 　4.4Problems 5 American Options 　5.1Characterization of the Optimal Exercise Boundaries 　　5.1.1American Options on an Asset Paying Dividend Yield 　　5.1.2Smooth Pasting Condition. 　　5.1.3Optimal Exercise Boundary for an American Call 　　5.1.4Put-Call Symmetry Relations. 　　5.1.5American Call Options on an Asset Paying Single Dividend 　　5.1.6One-Dividend and Multidividend American Put Options 　5.2Pricing Formulations of American Option Pricing Models 　　5.2.1Linear Complementarity Formulation 　　5.2.2Optimal Stopping Problem 　　5.2.3Integral Representation of the Early Exercise Premium 　　5.2.4American Barrier Options 　　5.2.5American Lookback Options 　5.3Analytic Approximation Methods 　　5.3.1Compound Option Approximation Method 　　5.3.2Numerical Solution of the Integral Equation 　　5.3.3Quadratic Approximation Method 　5.4 Options with Voluntary Reset Rights 　　5.4.1Valuation of the Shout Floor 　　5.4.2Reset-Strike Put Options 　5.5Problems 6 Numerical Schemes for Pricing Options 7 Interest Rate Models and Bond Pricing 8 Interest Rate Derivatives: Bond Options, LIBOR and Swap Products References Author Index Subject Index

章节摘录

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《金融衍生品数学模型(第2版)》是由世界图书出版公司出版的。

用户评论 (总计10条)

•   这本书里介绍了很多有关金融衍生品的数学模型，需要较强的数学知识，而且还是英文，需要慢慢啃
•   纸质还行 应该是正品吧 英文版 看着挺吃力 尤其对于一个完全没有金融基础的人来说~~所以我说书是好书 我看不太懂 又买了别的~~
•   虽然为影印版 但质量很好 很清晰 适合作为研究生的教材
•   帮弟弟买的 很好
•   公认的经典书籍
•   帮老公买的~
•   哈哈，印刷还可以，相对于原版也比较实惠，就是郭老师说他亏大了。。。。。。
•   内容比较全面，但证明不是很详细。比如伊藤公式的证明，太过于简洁
•   很不错 就是字体小了点 但不影响阅读 赞一个 快递速度也可以
•   湖大金融数学硕士标准教材。表述严谨的教材不少，很难找到像这样的一本启发读者从金融角度思考问题的读物，比Karatzas,Shreve的书写得更好。作者是香港科技大学金融数学专业教授。印刷质量不太好，字太小。