American-Style Derivatives: Valuation and Computation

Jérôme Detemple

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

MAA Review
Table of Contents

[Reviewed by

Ita Cirovic Donev

, on

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