The field of financial mathematics is expanding. Therefore, a good book on the introduction to mathematical finance will be appealing to academics and practitioners alike, despite the presence of a large number of existing texts in this area. The book under review may certainly be classed as an introductory text. It is specifically themed to explain the basic financial and mathematical concepts used in modeling and hedging.
The book is composed of 11 chapters. The first six chapters deal with the fundamentals of modelling and pricing equity derivatives using lattice tree and continuous‐time methods. The mathematics here are kept at a level which is not too technical, hence making the book accessible to a wide audience. In some cases, the mathematical properties are provided without formal proof; instead heuristic intuition is given to explain them. Another strong point of the book is its detailed step‐by‐step derivation of some mathematical equations. For instance, I enjoy reading the clear derivation of the Black‐Scholes closed‐form solution for European call option; its derivation is presented in a manner different from other books on introductory financial mathematics. Similarly, I find the heuristic derivation of the lognormal (Geometric Brownian Motion) model for stock refreshing.
Chapter 7 contains issues related to hedging. Delta hedge is discussed at length, but the roles of other important Greeks (measures of the sensitivity of a derivative to a change in an underlying parameter), most notably vega (a measure of sensitivity to volatility), are either not presented or merely discussed superficially. Personally, I would prefer more than a brief excursion to vega hedge, given the well‐known phenomena of the “volatility smile” (the U‐shaped pattern that can be obtained when implied volatility is plotted against strike prices) and that hedging is one of the main themes of the book.
Chapters 8 and 9 focus on modeling interest‐rate and bond pricing. Two standard models – Ho‐Lee and Vasicek – are discussed. Although both models are treated in detail, there is no discussion on the strengths and weaknesses of the respective models. In addition, I wish the chapters could have described alternative models such Cox‐Ingersoll‐Rubinstein and Hull‐White, which offer considerable improvement over the Ho‐Lee and Vasicek models.
Chapter 10 concentrates on modeling and pricing foreign exchange options. The derivation of the partial differential equation for pricing currency options via the Garman‐Kohlhagen model is elegant.
The last chapter, Chapter 11, deals with international political risk and credit derivatives. This chapter is commendable; it covers political risk and pricing international credit risk premiums using the Merton structural model and Jarrow‐Lando‐Turnbull framework. However, in my opinion, credit risk modeling is such a complicated issue that it is insufficient to treat it in one small chapter. Since the book primarily focuses on modeling market risk, the discussion of credit risk modeling could have been omitted without losing too much from the overall exposition.
To recapitulate, the book is a worthwhile contribution to the literature. Its main weakness is that perhaps it tries to cover too much, and in doing so, treats some issues less than satisfactorily. Its main strength is that it provides an introduction to mathematical finance at a level that is not too technical. Indeed, it is very successful in achieving this outcome. Therefore, I believe prospective undergraduate students of financial mathematics will find life much easier by reading the book.
