American-Style Derivatives: Valuation and Computation

American-Style Derivatives: Valuation and Computation

by Jerome Detemple
     
 

ISBN-10: 158488567X

ISBN-13: 9781584885672

Pub. Date: 11/14/2005

Publisher: Taylor & Francis

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

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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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Product Details

ISBN-13:
9781584885672
Publisher:
Taylor & Francis
Publication date:
11/14/2005
Series:
Chapman and Hall/CRC Financial Mathematics Series
Edition description:
New Edition
Pages:
248
Product dimensions:
6.20(w) x 9.30(h) x 0.80(d)

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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