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2019 | Book

Stochastic Dominance Option Pricing

An Alternative Approach to Option Market Research

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About this book

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.

Table of Contents

Frontmatter
Chapter 1. Stochastic Dominance: Introduction
Abstract
Stochastic dominance is a concept about choice under risk that was originally derived from the economics literature for the ordering of uncertain prospects by a particular set of investors. This chapter reviews the early definitions and applications, which started in 1962 with a contribution in the economics literature by Quirk and Saposnik and expanded into mathematics, finance and possibly other fields as well. It focuses on the stochastic dominance results that have implications for the study of option markets, including valuable econometric tests of pairwise comparisons of time series.
Stylianos Perrakis
Chapter 2. Stochastic Dominance Option Pricing I: The Frictionless Case
Abstract
This chapter presents the stochastic dominance (SD) approach to option pricing in frictionless markets, which was developed piecemeal from the outset in a discrete time context in a series of articles published in the mid-1980s. It derives multiperiod bounds for call and put options in a discrete time context, valid for any distribution. The bounds yield the Black-Scholes-Merton option price for both index and equity options when the underlying asset returns converge to any type of univariate diffusion when the time partition tends to 0. They also converge to tight bounds for both index and equity option prices when the underlying distribution includes rare events. It is shown that the index bounds can also explain several failures of the alternative equilibrium models based on a representative investor in the rare events case. Last, the SD frictionless bounds methodology is shown to produce useful results when applied to financial instruments issued by the insurance industry and indexed on catastrophe events.
Stylianos Perrakis
Chapter 3. Proportional Transaction Costs: An Introduction
Abstract
This chapter reviews the limited literature on option pricing in the presence of transaction costs outside the stochastic dominance (SD) approach. It starts by pointing out the importance of the topic, given the indeterminacy in defining the “true” price of a traded option because of the wide bid-ask spreads observed in the option markets. It then summarizes the studies that demonstrate the failure of the no arbitrage approach even when the underlying market is complete and there are transaction costs in trading the underlying asset. Last, it presents the generic investor’s dynamic asset allocation problem between a risky and a riskless asset given proportional transaction costs on the risky asset and derives the no transaction zone when the dynamics of the risky asset tend to diffusion or jump diffusion. These are inputs for the application of the SD approach to option pricing under transaction costs.
Stylianos Perrakis
Chapter 4. Stochastic Dominance Option Pricing II: Option Bounds Under Transaction Costs
Abstract
This chapter presents the available theoretical results for the valuation of individual index and index futures options under proportional transaction costs. These include the reservation write (upper) bounds on prices for European and American call options and the reservation purchase (lower) bounds for European and American put option prices, whose violations can generate riskless profits. They also include the reservation purchase (lower) bounds for European and American call options, which are, however, specific to the assumed trading time partition. It is also shown that these call option lower bounds converge to an elegant continuous time limit.
Stylianos Perrakis
Chapter 5. Stochastic Dominance Option Pricing: Empirical Applications
Abstract
This chapter reviews the rather sparse set of empirical studies that apply stochastic dominance (SD) to index option markets. This set also forms the quasi-totality of empirical studies in the option market that recognize transaction costs and use the observed option bid and ask prices as data. These SD studies include the following documented anomalies in many cross-sections of the S&P index options: the non-existence of a pricing kernel capable of pricing the entire cross-section of observed European option prices; the violation of the reservation write and reservation purchase prices by, respectively, observed European bid and ask option prices; the violations of the reservation write prices by the observed call bid prices of American futures options and the validation of the SD relation by out-of-sample tests. Last, they also include a method for deriving zero-net-cost European option portfolios that increase the expected return of an index while reducing its risk and indicate the existence of such portfolios in most cross-sections of S&P 500 options.
Stylianos Perrakis
Chapter 6. Stochastic Dominance and Further Theoretical and Empirical Option Research
Abstract
This chapter starts by examining the ability of stochastic dominance (SD) theory to price options in the presence of randomly changing volatility of index returns in the frictionless economy or, failing that, the robustness of the SD empirical results to such dynamics. It then applies the SD approach to several alleged empirical anomalies such as the overpriced puts and straddles derived in no arbitrage-equilibrium models of the option markets. Last, it presents several topics of suggested empirical option research that rely on or can be explored by the SD principles introduced in this book. These topics include a suggested model of the intermediation market for index options that can derive the bid-ask spread under certain assumptions, and the pricing of options when there are behavioral elements in an investor’s utility function in making choices under risk.
Stylianos Perrakis
Chapter 7. Conclusions
Abstract
This concluding chapter revisits some of the themes noted in the Preface in a more general context, positioning them into the realm of the entire body of knowledge known today as Finance, whose origins are in the seminal 1952 article of Harry Markowitz. It focuses on the assumptions underlying the dominant no arbitrage-equilibrium model of asset pricing in the frictionless economy when applied to the underlying asset and corresponding option markets. It argues that many of these assumptions have persisted for many years in spite of their lack of realism and their model’s inability to accommodate observed empirical facts. Last, it notes that stochastic dominance is a more general approach to option pricing that is based on fewer assumptions and can resolve several of these empirical contradictions.
Stylianos Perrakis
Backmatter
Metadata
Title
Stochastic Dominance Option Pricing
Author
Prof. Stylianos Perrakis
Copyright Year
2019
Electronic ISBN
978-3-030-11590-6
Print ISBN
978-3-030-11589-0
DOI
https://doi.org/10.1007/978-3-030-11590-6