金融数学--衍生产品定价引论（英文影印版）

　　金融数学的核心内容之一就是衍生产吕的定价。本书涉足隐藏在衍生证券定价、结构和套期保值背后的数学，严格而又通俗。作者用易于市场实践者理解的方式介绍了新的诸如鞅、测度变换等概念和heath-jarrow-morton模型。从借助于二叉树的离散时间套期保值开始，进一步推广到连续时间股票模型(包括black-scholes模型)。本书突出了可实践性，包括了股票、货币和利率市场的诸多例子，并提供了基于实际数据绘制的图形。附录中提供了关于概率和金融概念的术语表。
　　 本书作为金融数学的基础教材，适用于相关专业的本科生和研究生课程。也可供金融行业的市场实践者、定量分析师和衍生品交易者等相关领域专业人士参考。

the parable of the bookmaker
chapter 1 introduction
1.1 expectation pricing
1.2 arbitrage pricing
1.3 expectation vs arbitrage
chapter 2 discrete processes
2.1 the binomial branch model
2.2 the binomial tree model
2.3 binomial representation theorem
2.4 overture to continuous models
chapter 3 continuous processes
3.1 continuous processes
3.2 stochastic calculus
3.3 it6 calculus
3.4 change of measure - the c-m-g theorem
3.5 martingale representation theorem
3.6 construction strategies
3.7 black-scholes model
3.8 black-scholes in action
chapter 4 pricing market securities

　　Notoriously, works of mathematical finance can be precise, and they can be comprehensible. Sadly, as Dr Johnson might have put it, the ones which are precise are not necessarily comprehensible, and those comprehensible are not necessarily precise.
　　But both are needed. The mathematics of finance is not easy, and much market practice is based on a soft understanding of what is actually going on. This is usually enough for experienced practitioners to price existing contracts, but often insufficient for innovative new products. Novices, managers and regulators can be left to stumble around in literature which is ill suited to their need for a clear explanation of the basic principles. Such 'seat of the pants' practices are more suited to the pioneering days of an industry, rather than the mature $15 trillion market which the derivatives business has become.
　　On the academic side, effort is too often expended on finding precise answers to the wrong questions. When working in isolation from the market, the temptation is to find analytic answers for their own sake with no reference to the concerns of practitioners. In particular, the importance of hedging both as a justification for the price and as an important end in itself is often underplayed. Scholars need to be aware of such financial issues, if only because some of the very best work has arisen in answering the questions of industry rather than academe.
　　Guide to the chapters
　　Chapter one is a brief warning, especially to beginners, that the expected worth of something is not a good guide to its price. That idea has to be shaken off and arbitrage pricing take its place.
　　Chapter two develops the idea of hedging and pricing by arbitrage in the discrete-time setting of binary trees. The key probabilistic concepts of conditional expectation, martingales, change of measure, and representation are all introduced in this simple framework, accompanied by illustrative examples.
　　Chapter three repeats all the work of its predecessor in the continuous-time setting. Brownian motion is brought out, as well as the It6 calculus needed to manipulate it, culminating in a derivation of the Black-Scholes formula.
　　Chapter four runs through a variety of actual financial instruments, such as dividend paying equities, currencies and coupon paying bonds, and adapts the Black-Scholes approach to each in turn. A general pattern of the distinction between tradable and non-tradable quantities leads to the definition the market price of risk, as well as a warning not to take that name too seriously. A section on quanto products provides a showcase of examples.
　　Chapter five is about the interest rate market. In spirit, a market of bonds is much like a market of stocks, but the richness of this market makes it more than just a special case of Black-Scholes. Market models are discussed with a joint short-rate/HJM approach, which lies within the general continuous framework set up in chapter three. One section details a few of the many possible interest rate contracts, including swaps, caps/floors and swaptions. This is a substantial chapter reflecting the depth of financial and technical knowledge that has to be introduced in an understandable way. The aim is to tell one basic story of the market, which all approaches can slot into.
　　Chapter six concludes with some technical results about larger and more general models, including multiple stock n-factor models, stochastic numeraires, and foreign exchange interest-rate models. The running link between the existence of equivalent martingale measures and the ability to price and hedge is finally formalised.
　　A short bibliography, complete answers to the (small) number of exercises, a full glossary of technical terms and an index are in the appendices.
　　How to read this book
　　The book can be read either sequentially as an unfolding story, or by random access to the self-contained sections. The occasional questions are to allow practice of the requisite skills, and are never essential to the development of the material.
　　A reader is not expected to have any particular prior body of knowledge, except for some (classical) differential calculus and experience with symbolic notation. Some basic probability definitions are contained in the glossary, whereas more advanced readers will find technical asides in the text from time to time.
　　Acknowledgements
　　We would like to thank David Tranah at CUP for politely never mentioning the number of deadlines we missed, as well as his much more invaluable positive assistance; the many readers in London, New York and various universities who have been subjected to writing far worse than anything remaining in the finished edition. Special thanks to Lorne Whiteway for his help and encouragement.
　　Martin Baxter
　　June 1996
　　Andrew Rennie