Derivative Securities: The Complete Investor's Guide. Robert Jarrow and Stuart Turnbull. International Thomson Publishing. $34.95, paperback.

Reviewed by Edward Berman

In recent years, there has been a virtual explosion of books dedicated to the derivatives markets and valuation theory. Just a few years ago, a curious bystander had hardly any choice of texts dedicated to the option pricing, Black-Scholes-Merton analysis or modeling of the term structure of interest rates. Most books focused on the institutional aspects of the fixed-income markets or required a high level of mathematical training. In comparison, the books now being brought out try to bridge the gap between financial theory and the needs of practitioners. These include titles by derivatives luminaries such as John Hull, Robert Jarrow, Martin Baxter, Sheldon Ross, Paul Wilmott and others. The second edition of Derivative Securities by Jarrow and Stuart Turnbull fits comfortably in this trend.

What makes the book stand out from the crowd is its stress on understanding rather than rigorous theory. If your goal is to learn how to build and calibrate a term structure model for interest rates, this isn't the title for you. But if you want to understand the complexities and principles underlying dynamic pricing, you'd be hard-pressed to find a better book. This easy-to-understand text is aimed at those without much prior knowledge of the fixed-income markets and will be a valuable addition to the bookshelves of market practitioners, risk managers, students and anyone interested in a better understanding of how the derivatives markets operate.

The volume's focus is on a wide range of cash and derivative products, in the fixed-income and equity worlds. All explanations are brief enough to keep readers focused, but general enough not to sacrifice the quality of discussion. Multiple examples positioned strategically throughout the text help in understanding the theoretical concepts.

The first three chapters introduce futures, forwards and options. The emphasis is on simple no-arbitrage pricing relationships and the institutional aspects of the markets. Information on other markets occupies the later chapters of the book. Chapter 11 tackles foreign exchange options, Chapter 12 deals with equities, and Chapters 13 and 14 go into finer detail on interest rate futures and swaps.

Where the book shines is in its discussion of the application of binomial models to the pricing of derivatives. The binomial model is simple enough not to overwhelm readers with arcane mathematics, and rich enough to illustrate crucial aspects of contemporary valuation theory. Jarrow and Turnbull wisely avoid the temptation to use a more sophisticated model. They touch briefly on the HJM model in Chapter 16, but those interested in HJM would be better served by a number of other books available on the subject. The binomial model is introduced early in the book, and is used to explain American vs. European options, futures and forwards on instruments ranging from foreign exchange to stock indices and interest rates. While keeping explanations simple and easy to understand, Jarrow and Turnbull address the many subtle points of lattice-based pricing. A good example is their discussion in chapter seven of the lattice discontinuity arising from stock dividend payments.

No introductory book on derivatives could be complete without a discussion of the Black-Scholes-Merton model. Derivative Securities doesn't break with tradition in this regard, dedicating two chapters to the Black-Scholes-Merton analysis. Here, again, the emphasis is more on understanding and less on mathematics. But in taking this approach, Jarrow and Turnbull sacrifice some clarity in explaining the famous formula. They also could have spent more time explaining the parameters of the equation and the sensitivity of price on the parameters. To be fair to the book, however, many of these topics are covered later within the framework of the binomial model, and the account of assumptions underlying Black-Scholes-Merton is probably one of the best seen so far.

Another area that warranted more background was the foundation of dynamic asset pricing theory. Jarrow and Turnbull dedicate two chapters to a discussion of random processes, probability distributions, the martingale measure and risk-neutral valuation, but the authors try to work around these math-rich topics primarily by avoiding them. Some formal introduction into stochastic calculus would have helped the reader better understand the later chapters, since some of them are thick with formulations based on partial differential equations. Instead, the authors chose to concentrate theoretical issues related to pricing under the "Formalization” heading found in nearly every subchapter.

One area where Derivative Securities excels is its coverage of the frequently neglected topic of reconciling pricing models with the real world. The authors devote two chapters to what they crisply call "model misspecification.” They investigate thoroughly the shortcomings of delta and delta/gamma hedging by applying the Black-Scholes-Merton and HJM models to various derivative instruments. They also sketch out the modeling of the term structure of interest rates, with excellent illustrations on building binomial- and HJM-based models. As is the case for the book at large, the emphasis is on explaining the underlying principles rather than giving a blueprint for calibrating term structure models to real market data.

The authors also deserve kudos for a chapter dedicated to the valuation of the credit component of the fixed-income market. This relatively new field of financial theory is currently in its development stage, and Jarrow and Turnbull are well-known and well-regarded in the field for their multiple publications on the subject over the last several years. The book's description of credit risk follows the authors' groundbreaking paper from 1995, with an exceptional discussion of pricing risky debt. Derivative Securities is one of the few books in the market today that offers a clear explanation of the pricing of credit derivatives.

Edward Berman is an associate at Capital Market Risk Advisors.