Equity Derivatives- Theory and Applications by Marcus Overhous, Andrew Ferraris, et al. (John Wiley 2002)

The book consists of nine chapters. In the first five chapters, we find an overview of the theory and practice of equity derivatives, and the last four chapters deal with computer implementations.

Chapter 1 summarizes the basic mathematical concepts and financial interpretations of the theory of stochastic process and stochastic calculus which are used in the book. To understand these chapters, the reader is assumed to be familiar with basic probability theory and statistics.

Chapter 2 deals with pricing and hedging in incomplete markets; variance– optimal pricing, super hedging, and quantitative hedging. Several helpful examples are given to illustrate the concepts and the relationships between equivalent martingale measures. The Heston and the Hill-While models are introduced for the volatility of currency and interest rate options.

Chapter 3 is a primer on Levy processes; some of their applications in modeling pricing of derivative products are given. For their numerical solutions the authors discuss the Fast Fourier Transform, Monte Carlo simulation and the Finite Difference Methods (FDM). This chapter contains several helpful examples.

Chapter 4 examines several pricing models and discretization of their corresponding systems of parabolic partial differential equations. For numerical solution the authors promote and discuss FDM because they are extensively used in applied mathematics. In the second part of the chapter, several volatility models are reviewed.

Chapters 5 examines convertible bond models. The effect of interest rate stochasticity and volatility skew on convertible bond valuation are analyzed. In the chapter the theory and practice of convertible bond asset swaps are discussed. These kinds of swaps permit the separation of equity risk and credit risk in the convertible bond, which allows different market segments greater flexibility in portfolio management.

Chapters 6 and 7 outline the computer system XML (Extensible Markup Language) for data representation and transmission and SDAP (Simple Object Access Protocol), which permits quick delivery of systems to the desktop. Chapter 8 surveys Web applications. In Chapter 9, the final chapter, there are examples for algorithms and software design in discrete hedging and volatility for certain markets.

A notable feature of the book is that about one this of its is spend on the availability and applicability of computer packages in finance, particularly pricing and hedging of derivatives. However, it is unclear what audience was intended for the text. It is certainly not for beginners, yet it is too superficial to be for experts. In the preface the authors inform us that they have written two previous texts on the same topics, yet nowhere in this book do they reference their previous work. Are they being deliberately repetitive, one wonders?

The author use acronyms a great deal in the text, but there is no glossary to translate these into English. Those that are in the index do not appear in correct alphabetical order! This is more than minimally sloppy This book may be useful for highly literate economists or mathematicians who want a deep dive into the world of finance.