This paper examines the stochastic dominance efficiency in the presence of transaction costs for Samp;P 500 index futures call and put options by estimating bounds on reservation write and reservation purchase prices and then verifying whether the observed option prices satisfy them. The bounds are estimated from data on past realizations of the underlying asset and under various data-based assumptions about the investor-assumed distribution of that asset. The bounds are then compared to observed market prices and several violations are identified under all distributional assumptions, although these violations are relatively few under forward-looking distributions. The paper then derives trading strategies that exploit these violations and increase expected utility for any risk averse investor. It develops a metric that evaluates the increase in expected utility for any given investor within a certain utility class and links it with the traditional second degree stochastic dominance criterion. Last, it demonstrates by out-of-sample tests with realized underlying asset prices that these strategies to exploit the mispricing of index futures options do indeed improve risk-adjusted returns for risk averse investors.

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.

In the first essay American call and put options on the S & P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (CP, 2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing and also strongly supportive of the CP bounds as screening mechanisms for mispriced options. The second essay introduces a result for call lower bound more powerful that the one applied in the first part of this thesis. The Proposition 5 call lower bound in Constantinides and Perrakis (2002) is shown to have a non-trivial limit as the time interval tends to zero. This establishes the bound as the first call lower bound known in the literature on derivative pricing in the presence of transaction costs with a non-trivial limit. The bound is shown to be tight even for a low number of time subdivisions. Novel numerical methods to derive recursive expectations under a Markovian but non-identically distributed stochastic process are presented. The third essay relaxes an assumption in the first part of this thesis on the optimal trading policy in the presence of transaction costs. We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion instead of a simple diffusion process. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in an earlier published work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.

American options on the S & P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2007) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out of sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk averse investor holding the market and cash, net of transaction costs and bid ask spreads. The results are economically significant and robust.

This paper investigates the multi-period upper bound on the European call price in the presence of transaction costs derived by Constantinides-Perrakis (2002). Numerical results verifying an assumption of the monotonictity of wealth of the call writer in the underlying asset on which the Constantinides-Perrakis (2002) model relies are derived, and it is shown that the assumption is satisfied for relatively small ratios of stock to option account. The classic second order stochastic dominance argument is applied to the dynamic trading in discrete time in the S & P 500 options under the portfolio selection criteria in the presence of transaction costs. It is shown that the improvement in expected utility does occur under the prescribed investment policy in the S & P 500 calls whose prices exceed the bound. Under the lognormality of the S & P 500 price process, the quantitative improvement in expected utility is derived.

This book is devoted to investment decision-making under uncertainty. The book covers three basic approaches to this process: the stochastic dominance approach; the mean-variance approach; and the non-expected utility approach, focusing on prospect theory and its modified version, cumulative prospect theory. Each approach is discussed and compared. In addition, this volume examines cases in which stochastic dominance rules coincide with the mean-variance rule and considers how contradictions between these two approaches may occur.

The Efficient Market Hypothesis believes that it is impossible for an investor to outperform the market because all available information is already built into stock prices. However, some anomalies could persist in stock markets while some other anomalies could appear, disappear and re-appear again without any warning. A Special Issue on "Efficiency and Anomalies in Stock Markets" will be devoted to advancements in the theoretical development of market efficiency and anomaly in the Stock Market, as well as applications in Stock Market efficiency and anomalies.