金融建模中的鞅方法

出版时间：2007-5  出版社：北京世图  作者：姆斯拉  页数：636  
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内容概要

　　The origin of this book can be traced to courses on financial mathematics taught by us at the University of New South Wales in Sydney， Technical University of Warsaw （Politechnika Watszawska） and Institut National Polytechnique de Grenoble. Our initial aim was to write a short text around the material used in two one-semester graduate courses attended by students with diverse disciplinary backgrounds （mathematics， physics， computer science， engineering， economics and commerce）. The anticipated diversity of potential readers explains the somewhat unusual way in which the book is written. It starts at a very elementary mathematical level and does not assume any prior knowledge of financial markets. Later， it develops into a text which requires some familiarity with concepts of stochastic calculus （the basic relevant notions and results are collected in the appendix）. Over time， what was meant to be a short text acquired a life of its own and started to grow. The final version can be used as a textbook for three one-semester courses one at undergraduate level， the other two as graduate courses.

书籍目录

Preface of the First EditionPerface of the Second EditionPartⅠ.Psot to the Futures Markets1.An Introduction to Financial Derivatives1.1 Options1.2 Futures Contracts and Options1.3 Forward Contracts1.4 Call and Put Spot Options1.4.1 One-period Spot Market1.4.2 Replicating Portfolios1.4.3 Martingale Measure for a Spot Market1.4.4 Absence of Arbitrage1.4.5 Optimality of Replication1.4.6 Put Option1.5 Futures Call and Put Options1.5.1 Futures Contracts and Futures Prices1.5.2 One-period Futures Market1.5.3 Martingale Measure for a Futures Market1.5.4 Absence of Arbitrage1.5.5 One-period Spot/Futures Market1.6 Forward Contracts1.6.1 Forward Price1.7 Options of American Style2.The Cox-Ross-Rubinstein Model2.1 The CRR Model of a Stock Price2.1.1 The CRR Option Pricing Formula2.1.2 The Black-Scholes Option Pricing Formula2.2 Probabilistic Approach2.2.1 Martingale Measure2.2.2 Risk-neutral Valuation Formula2.3　the Blace -Scholes Option Pricing Formula2.4 Valuation of American Options2.4.1 American Call Preface2.4.2　American Put Options2.4.3 America Claim2.5 Options on a Dividend-paying Stock2.6 Finite Spot Markets2.6.1 Self-financing Trading Strategies2.6.2 Arbitrage Opportunities2.6.3 Arbitrage Price2.6.4 Risk-neutral Valuation Formula2.6.5 Price Systems2.6.6 Completeness of a Finite Market2.6.7 Change of a Numeraire2.7 Finite Futures Markets2.7.1 Self-financing Futures Strategies2.7.2 Martingale Measures for a Futures Market2.7.3 Risk-neutral Valuation Formula2.8 Futures Prices Versus Forward Prices2.9 Discrete-time Models with Infinite State Space3.Benchmark Models in Continuous Time3.1 The Black-Scholes Model3.1.1 Risk-free Bond3.1.2 Stock Price3.1.3 Self-financing Trading Strategies3.1.4 Martingale Measure for the Spot Market3.1.5 Black-Scholes Option Pricing Formula3.1.6 Case of Time-dependent Coefficients3.1.8 Put-Call Parity for Spot ODtions3.1.9 Black-Scholes PDE ：3.1.10 A Riskless Portfolio Method3.1.11 Black-Scholes Sensitivities3.1.12 Market Imperfections3.1.13 Numerical Methods3.2 A Dividend-paying Stock3.2.1 Case of a Constant Dividend Yield3.2.2 Case of Known Dividends3.3 Bachelier Model3.3.1 Bachelier Option Pricing Formula3.3.2 Bachelier‘s PDE……PartⅡ Fixes-income MarketsPartⅢ APPENDICESReferencesIndex

章节摘录

　　We shall now describe， following Hull （1997）， the basic features of tradi-tiorial stock and options markets， as opposed to computerized online trading.The most common system for trading stocks is a specialist system， Underthis system， an individual known as the specialist is responsible for beinga market maker and for keeping a record of limit orders - that is， ordersthat can only be executed at the speafied price or a more favorable price.Options usually trade under a market maker system. A market maker for agiven option is an individual who will quote both a bid and an ask price onthe option whenever he is asked to do so. The bid price is the price at whichthe market maker is prepared to buy and the ask price is the price at whichhe is prepared to sell. At the time the bid and ask prices are quoted， themarket maker does not know whether the trader who asked for the quoteswants to buy or sell the option. The amount by which the ask exceeds thebid is referred to as the bid-ask spread. To enhance the efficiency of trading，the exchange may set upper limits for the bid-ask spread.　　The existence of the market maker ensures that buy and sell orders canalways be executed at some price without delay. The market makers them-selves make their profits from the bid-ask spread. When an investor writesoptions， he is required to maintain funds in a margin account. The size of themargin depends on the circumstances， e.g.， whether the option is covered ornaked - that is， whether the option writer does possess the underlying sharesor not. Let us finally mention that one contract gives the holder the rightto buy or sell 100 shares; this is convenient since the shares themselves areusually traded in lots of 100.　　……