This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.

Stylianos Perrakis is the Royal Bank of Canada Distinguished Professor of Financial Derivatives at the John Molson School of Business, Concordia University, Canada. He has taught as a regular or visiting professor at universities in the USA, France, Switzerland and Greece. He is a Fellow of the Royal Society of Canada and the editor or associate editor of several finance and financial engineering journals. Perrakis is the author of Canadian Industrial Organization (Prentice-Hall Canada ,1990) and co-author of the textbook Investments, which is currently in its 8th edition.

1;Dedication;5 2;Foreword;6 3;Preface;8 3.1;References;12 4;Contents;14 5;List of Figures;15 6;List of Tables;19 7;Chapter 1: Stochastic Dominance: Introduction;22 7.1;1.1 Definition;23 7.2;1.2 Risk and Second-Degree Stochastic Dominance;26 7.3;1.3 Empirical Applications and Portfolio Selection Under SSD or TSD;31 7.4;1.4 Empirical Tests of Stochastic Dominance;33 7.5;1.5 Summary and Conclusions;36 7.6;References;37 8;Chapter 2: Stochastic Dominance Option Pricing I: The Frictionless Case;39 8.1;2.1 SD Option Pricing by Pairwise Comparisons;40 8.2;2.2 SD Option Pricing: The Linear Programming Approach;50 8.3;2.3 The Frictionless SD Bounds in Continuous Time for Diffusion;56 8.3.1;Index Options;58 8.3.2;Equity Options;60 8.4;2.4 The Frictionless SD Bounds in Continuous Time for Jump Diffusion I: Index Options;65 8.4.1;Upper and Lower Bound for Jump Diffusion;66 8.4.2;Numerical Results;74 8.4.3;Stochastic Dominance and Equilibrium Option Prices;77 8.5;2.5 The Frictionless SD Bounds in Continuous Time for Jump Diffusion II: Equity Options;82 8.6;2.6 An Important Application of Jump Diffusion: Catastrophe (CAT) Derivatives;88 8.6.1;The Valuation Model for Convex Payoffs Without a CAT Futures Market;90 8.6.2;Claims with Non-Convex Payoffs but with a CAT Futures Market;93 8.6.3;Catastrophe (CAT) Bonds and Reinsurance Contracts;97 8.7;2.7 Summary and Conclusions;99 8.8;References;102 9;Chapter 3: Proportional Transaction Costs: An Introduction;106 9.1;3.1 No Arbitrage Under Transaction Costs;109 9.1.1;Replicating Portfolios;110 9.1.2;Super Replication and the Failure of No Arbitrage;114 9.2;3.2 Portfolio Selection Under Proportional Transaction Costs;116 9.2.1;Asset Allocation in Discrete Time;116 9.2.2;The No Trade Region in Continuous Time for an Infinite Investment Horizon;118 9.2.3;What Happens When the Horizon Is Finite?;121 9.3;3.3 Simultaneous Equilibrium in the Underlying and Option Markets;122 9.4;3.4 Summary and Conclusions;126 9.5;References;127 10;Chapter 4: Stochastic Dominance Option Pricing II: Option Bounds Under Transaction Costs;129 10.1;4.1 European Index Option Bounds Under Transaction Costs;131 10.1.1;The Upper Bound of a European Call Option and the Lower Bound of a European Put Option;133 10.1.2;The Lower Bound of a European Call Option;140 10.2;4.2 American Index Option Bounds Under Transaction Costs;153 10.2.1;The Upper Bound of an American Index Call Option;154 10.2.2;The Lower Bound of an American Index Put Option;158 10.2.3;Bounds on the Prices of American Index Futures Options as in Theorems 5 and 6;162 10.2.4;The Lower Bound of an American Call Index and Index Futures Option;165 10.3;4.3 Summary and Conclusions;168 10.4;4.4 Mathematical Appendix;170 10.4.1;Proof of Lemma 1;170 10.4.2;Proof of Theorem 3;172 10.4.3;Proof of Theorem 4;178 10.4.4;Proof of Lemma 2;181 10.4.5;Proof of Theorem 5;182 10.4.6;Proof of Theorem 6;188 10.5;References;192 11;Chapter 5: Stochastic Dominance Option Pricing: Empirical Applications;194 11.1;5.1 Empirical Applications I: Pricing the Option Cross-Section Under Transaction Costs;196 11.2;5.2 Empirical Applications II: Individually Mispriced Options Under Transaction Costs;199 11.2.1;In-Sample Tests on Individual Options' Mispricing;199 11.2.2;Out-of-Sample Tests of Individual Options' Mispricing;200 11.3;5.3 Empirical Applications III: Mispriced Option Portfolios Under Transaction Costs;208 11.4;5.4 Mispriced Option Portfolios in the Frictionless Economy;215 11.4.1;Does a U-Shaped Pricing Kernel Explain the Anomalous OT Results?;217 11.4.2;The U-Shaped Kernel, the OT Portfolios and the "Anomalous" Straddles and Puts;220 11.5;5.5 Conclusions;222 11.6;References;223 12;Chapter 6: Stochastic Dominance and Further Theoretical and Empirical Option Research;226 12.1;6.1 Stochastic Dominance, Stochastic Volatility and GARCH;228 12.1.1;Stochastic Volatility;229 12.1.2;GARCH Asset Dynamics;234 12.2;6.2 Stochastic Dominance and Empirical Option Anomalies;240 12.2.1;The U-Shaped Pricin