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Publisher:

Chapman & Hall/CRC

Publication Date:

2006

Number of Pages:

232

Format:

Hardcover

Series:

Financial Mathematics Series 4

Price:

79.95

ISBN:

1-58488-567-X

Category:

Monograph

[Reviewed by , on ]

Ita Cirovic Donev

06/5/2006

*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.

INTRODUCTION

EUROPEAN CONTINGENT CLAIMS

Definitions

The Economy

Attainable Contingent Claims

Valuation of Attainable Claims

Claims Involving Negative Payoffs

The Structure of Contingent Claims' Prices

Changes of Numeraire and Valuation

Option and Forward Contracts

Markets with Deterministic Coefficients

Markets with Multiple Assets

Appendix: Proofs

AMERICAN CONTINGENT CLAIMS

Contingent Claims with Random Maturity

American Contingent Claims

Exercise Premium Representations

A Duality Formula: Upper Price Bounds

American Options and Forward Contracts

Multiple Underlying Assets

Appendix: Proofs

STANDARD AMERICAN OPTIONS

The Immediate Exercise Region

The Call Price Function

Early Exercise Premium Representation

A One-Dimensional Integral Equation

Hedging

Diffusion Processes

Floating Strike Asian Options

American Forward Contracts

Appendix: Proofs

BARRIER AND CAPPED OPTIONS

Barrier Options

Capped Options

Diffusion Processes

Appendix: Proofs

OPTIONS ON MULTIPLE ASSETS

Definitions, Examples and Literature

The Financial Market

Call Options on the Maximum of 2 Assets

American Spread Options

Options on an Average of 2 Assets

Call Options on the Minimum of 2 Assets

Options with n > 2 Underlying Assets

Appendix A: Derivatives on Multiple Assets

Appendix B: Proofs

OCCUPATION TIME DERIVATIVES

Background and Literature

Definitions

Symmetry Properties

Quantile Options

Parisian Options

Cumulative Parisian Contingent Claims

Step Options

American Occupation Time Derivatives

Multiasset Claims

Appendix: Proofs

NUMERICAL METHODS

Numerical Methods for American Options

Integral Equation Methods

Exercise Time Approximations: LBA-LUBA

Diffusion Processes

Other Recent Approaches

Performance Evaluation

Methods for Multiasset Options

Methods for Occupation Time Derivatives

Appendix: Proofs

Bibliography

Index

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