American-Style Derivatives

American-Style Derivatives : Valuation and Computation

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Description

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.show more

Product details

  • Hardback | 248 pages
  • 160 x 236.2 x 20.3mm | 476.28g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 18 black & white illustrations, 5 black & white tables
  • 158488567X
  • 9781584885672

Review quote

"... 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, USAshow more

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 Indexshow more