Every option considered

Derivatives are financial contracts whose value depends on the price of an underlying asset. A simple example is a forward contract that guarantees the interest rate for a borrowing to start in six months' time. Financial engineering consists of building new kinds of financial structures with various derivatives, to suit the needs of particular companies.

There are many books on derivatives: a search of Amazon.com brings up 392. There are also several books that have "financial engineering" in the title. The reason for this outpouring is that many professionals in finance do not understand derivatives, so authors try to meet that demand with simple and repetitive tomes. Although derivatives include forwards, futures, options and swaps, this book concentrates on options. It is a serious work that takes the reader all the way from the simplest of notions to the most complicated of recent models. In short, it is the most comprehensive and up-to-date textbook on options that I have seen.

Paul Wilmott has set out to write the textbook on the subject of options. The style is jocular, but the content is heavyweight. The aim is to use a mathematical approach at all times but to motivate the development of models with intuition and to use diagrams and spreadsheet solutions whenever possible. It sounds like an impossible mission. Who ever heard of a mathematician who could convey the intuition of a result to those (like myself) with a less complete training in the subject? Wilmott is an exception: he knows when a result is hard to understand and treats the reader in a sympathetic manner. Although the book is 50 chapters and 768 pages long, one does not feel overwhelmed, mainly because there is no tendency for successive chapters to become more difficult.

The book is organised in six parts. The first covers the basic mathematics and develops the Black/Scholes model and its variants. The second is concerned with path-dependent and non-standard (exotic) options. These include barriers, Asians, lookbacks, shouts and others. There are even American-style Parisian options (which the author thinks would have appealed to Henry Miller). The third part deals with deviations from the Black/Scholes world of perfect markets and smoothly diffusing prices. Here there is coverage of transactions costs, stochastic volatility, diffusion jumps and periodic crashes. Part four is concerned with interest-rate models, which are necessarily more difficult to understand but are treated simply. Part five covers risk measurement and management, including value-at-risk for derivatives and credit derivatives. Finally, part six gives a round-up of numerical methods. All chapters have very clear introductions and summaries, as well as extensive sets of questions. A CD accompanies the text.

For whom is the book written? At Pounds 25 it is an affordable textbook. It requires that students are not afraid of mathematics, and so is most suitable either for a second-level course on options or as a first course for students with a mathematical background. The university readership is final-year undergraduates or postgraduate students specialising in finance. This is also a book for the professional audience, and I cannot imagine any derivatives specialist in an investment bank who would not want to have the book available.

No book is perfect. The style will not suit everyone. It is unusual for a textbook to have a picture on the back cover of the author relaxing on his boat: one feels that he should have had a gin-and-tonic in his hand. The book is also focused on the valuation of options and gives only the nuts and bolts of financial engineering.

That does not tell us much about why there are so many different kinds of derivative, how they can be used and whether they contribute to our wellbeing in any way. As an example, there is a chapter on convertible bonds, but no discussion of why companies issue them. Other missing topics are so-called real options and the use of option prices to derive implied distributions (a practice followed by many central banks for their interest-rate forecasting).

This book is a splendid achievement and I am already recommending it to students who have a mathematical background.

Gordon Gemmill is professor of finance, Business School, City University.