金融衍生品數(shù)學(xué)模型

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.

內(nèi)容概要

本書旨在運(yùn)用金融工程方法講述模型衍生品背后的理論，作為重點(diǎn)介紹了對(duì)大多數(shù)衍生證券很常用的鞅定價(jià)原理。書中還分析了固定收入市場(chǎng)中的大量金融衍生品，強(qiáng)調(diào)了定價(jià)、對(duì)沖及其風(fēng)險(xiǎn)策略。本書從著名的期權(quán)定價(jià)模型的Black-Scholes-Merton公式開始，講述衍生品定價(jià)模型和利率模型中的最新進(jìn)展，解決各種形式衍生品定價(jià)問題的解析技巧和數(shù)值方法。目次：衍生品工具介紹；金融經(jīng)濟(jì)和隨機(jī)計(jì)算；期權(quán)定價(jià)模型；路徑依賴期權(quán)；美國期權(quán)；定價(jià)期權(quán)的數(shù)值方案；利率模型和債券計(jì)價(jià)；利率衍生品：債券期權(quán)、LIBOR和交換產(chǎn)品。

書籍目錄

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

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