American-Style Derivatives: Valuation and Computation

By Jackson, James | Journal of Risk and Insurance, December 2009 | Go to article overview

American-Style Derivatives: Valuation and Computation


Jackson, James, Journal of Risk and Insurance


American-Style Derivatives: Valuation and Computation, by Jerome Detemple, 2006, Chapman & Hall/CRC, Boca Raton, FL, pp. 248. ISBN: 978-1584885672

In his book American-Style Derivatives: Valuation and Computation, Jerome Detemple presents the subject areas of financial engineering and investment finance with "an extensive treatment of the theoretical and computational aspects of derivative securities pricing" (p. 1). While the author provides the reader with a comprehensive discussion of background theories and a review of the literature on derivative securities in general, the main focus of the text is on pricing and valuation of American-style derivative securities.

Financial engineers and finance professionals who are considering reading AmericanStyle Derivatives should be advised that Detemple has written a relatively short but rigorous book that is targeted toward readers who want to know how to price complex American-style derivative securities at an advanced level. While each chapter of the book offers background information and theories necessary to understand derivatives pricing theory and different option pricing models, most of the computational material is only accessible to readers who have mastered an advanced level of mathematical training. Further, the book concentrates on reviewing and expanding the discussion of the history and pricing of American-style derivatives rather than strategies for the use of derivative securities. Lastly, each chapter contains a wellorganized appendix that provides mathematical proofs of each equation featured in the book. However, each chapter is also packed with so many formulas, theories, lemmas, corollaries, and propositions that even an advanced student or professional may need to take pause and may consider searching for a more simple explanation of the concepts elsewhere.

For those readers seeking condensed background information on the development of the theory and computational aspects of derivative securities pricing, perhaps the most useful chapter of American-Style Derivatives is the introductory chapter, in this chapter, Detemple explains his approach to explaining derivative security pricing, in general, and its relation to recent improvements in computational methods used in American-style derivative pricing. The author surveys the history of option contracts use and discusses important milestones along the way to the current understanding of option pricing theory. From the early work of Bachelier (1900) that modeled the random behavior of asset prices to the more recent work of Black, Scholes, and Merton (Black and Scholes, 1973; Merton, 1973) (p. 2) and their development of modern option pricing theory, Detemple explains the development of derivative pricing theory in chronological order and in the order of significance to the field of finance.

From this foundation, Detemple continues his treatment of derivative securities' pricing methods by first reviewing the valuation methods of European-style contingent claims in Chapter 2 (p. 7), followed by an explanation and extension of the pricing of American-style derivatives based on the Ito price process and the general Brownian motion framework in Chapter 3 (p. 37). Chapter 4 is a discussion of plain-vanilla options, as well as more exotic options such as the floating strike price Asian option (p. 55), while Chapter 5 provides further explanation of the valuation of exotic options such as American-style barrier and capped option contracts using the Black-Scholes method (p. 85).

In Chapter 6, Detemple provides an examination of the concepts and pricing of multiple asset options, which include max-options, min-options, and spread-options (p. 107). Chapter 7 introduces the reader to the valuation of American- and Europeanstyle occupation time derivatives, which are valued based on the amount of time the underlying asset remains in a defined price range (p. 155). Finally, Chapter 8 provides an overview and explanation of the most recent developments in the numerical methods used to price and value American-style option agreements. …

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