*American-Style Derivatives* is a research-oriented book aimed at graduate students and researchers in the area of financial derivatives. Financial derivatives are a complex and demanding field in which advanced valuation methods are not only needed but required in every aspect. Detemple provides us with a detailed treatment of derivative securities pricing with an emphasis on American-style derivatives. The author pays much attention to the historical developments in the field by outlining historical as well as current research. This will be very helpful for first-time readers on American-style derivatives. As can be seen from the table of contents, Detemple covers general aspects of American derivatives but he also introduces some newer concepts such as occupational time derivatives.

Numerical methods for the valuation of derivatives are extremely important. Detemple covers numerical methods in one chapter, but only those methods relating to the concepts presented in the book. Hence, prior knowledge of numerical methods for the valuation of financial derivatives is needed.

Even though the book is written in a theorem-proof style all the proofs are presented in the appendices at the end of each chapter. Personally, I don't favor this style of writing, especially given that this is a research type book and not an applied one. The publisher claims that "The book is written so that the material is easily accessible not only to those with a background in stochastic processes and/or derivative securities, but also to those with a more limited exposure to those areas." I disagree. I think that one needs to be very versatile in stochastic processes and know, at least, the general concepts of derivative securities in order to effectively follow the text.

Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.