American-Style Derivatives: Valuation and Computation

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Overview

While the valuation of standard American option contracts has now achieved a fair degree of maturity, much work remains to be done regarding the new contractual forms that are constantly emerging in response to evolving economic conditions and regulations. Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with an emphasis on the valuation of American options on dividend-paying assets.

The book begins with a review of valuation principles for European contingent claims in a financial market in which the underlying asset price follows an Ito process and the interest rate is stochastic and then extends the analysis to American contingent claims. In this context the author lays out the basic valuation principles for American claims and describes instructive representation formulas for their prices. The results are applied to standard American options in the Black-Scholes market setting as well as to a variety of exotic contracts such as barrier, capped, and multi-asset options. He also reviews numerical methods for option pricing and compares their relative performance.

The author explains all the concepts using standard financial terms and intuitions and relegates proofs to appendices that can be found at the end of each chapter. 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.

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Editorial Reviews

From the Publisher
"… 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. … Given the depth and quality of the discussion in American-Style Derivatives, it is difficult to find fault either with the structure of the book or with the author’s treatment of the specific subject matter. The book is rich with explanations of the stochastic process and is rigorous in its treatment of the advanced computational methods that make derivative securities both complex to price and useful to those who can harness their power to manage financial risk and gain excess financial returns. … Detemple has an obvious talent for explaining, developing, and extending the computational methods involved in the pricing of derivative securities. …"
The Journal of Risk and Insurance, 2009, Vol. 76, No. 4

"This research monograph gives an excellent summary of recent research on the American option problem. … The subject matter at this level is unavoidably technical but the author maintains a good balance between rigor and intuition. The book concentrates on equity options rather than interest rate options, on pricing rather than hedging. Professor Detemple may not dig far but he digs deep."
—Short Book Reviews, December 2006

"There are numerous financial engineering texts that touch on American-style derivatives pricing. What Detemple's book does is focus on Americans. His approach combines the depth and insights of a monograph with the historical perspective and detailed citations of a survey of the literature. The book is well written, and concepts are intuitively motivated. The writing is technical, but it should be accessible to most any financial engineer. The author saves proofs for the ends of chapters. In most cases, these are one or two line thumbnails rather than full proofs. For an in-depth look at the literature on American-style derivatives pricing, this is the book to read."
—Glyn A. Holton, Contingency Analysis

"Jerome Detemple has written an excellent survey of the field of derivative securities of the 'American' type that can be exercised at any time before or at maturity. He covers extensively the probabilistic theory which underlies their valuation. He discusses in detail both 'plain' and 'exotic' contingent claims, including barrier, quantile, capped, multiple-asset, and occupation-time options. Finally, and perhaps most importantly, he presents recent results on the numerical computation of optimal exercise boundaries, hedging prices, and hedging portfolios. A considerable part of the monograph is based on the author's extensive research in this area.
The treatment is complete and authoritative, and the monograph will be valuable to both academics and practitioners with an interest in this area. Professor Detemple has done a great service, by presenting in this compact volume a great amount of scholarship and research that took place over the last two decades in this field."
—Professor Ioannis Karatzas, Columbia University, New York, USA

"The early exercise feature of American-Style Derivatives has enormous practical importance, and the same feature presents substantial theoretical and computational challenges. Professor Detemple's lucid and careful presentation represents the definitive treatment of the current state-of-the-art of this important subject. I highly recommend it for all students and researchers in the area."
—Professor Mark Broadie, Columbia University, New York, USA

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Product Details

Table of Contents

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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