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From stochastic dominance to Black–Scholes: An alternative option pricing paradigm

Research paper by Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-;mail: michael.oancea@business.uconn.edu<br>Stylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-;mail: perrakis@jmsb.concordia.ca

Indexed on: 13 May '16Published on: 05 Dec '14Published in: Risk and Decision Analysis



Abstract

This paper examines the relationship between option pricing models that use stochastic dominance concepts in discrete time, and the traditional arbitrage-based continuous time models. It derives multiperiod discrete time index option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution in which the market index is the single state variable. It then considers the limit behavior of these bounds as trading becomes progressively more frequent and the underlying asset tends to continuous time diffusion. It is shown that these bounds tend to the unique Black–Scholes–Merton option price. This result is extended to equity options by assuming a linear CAPM-type relationship between index and equity returns. Content Type Journal ArticlePages 99-112DOI 10.3233/RDA-140103Authors Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-mail: michael.oancea@business.uconn.eduStylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: perrakis@jmsb.concordia.ca Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Volume Volume 5 Journal Issue Volume 5, Number 2-3 / 2014 This paper examines the relationship between option pricing models that use stochastic dominance concepts in discrete time, and the traditional arbitrage-based continuous time models. It derives multiperiod discrete time index option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution in which the market index is the single state variable. It then considers the limit behavior of these bounds as trading becomes progressively more frequent and the underlying asset tends to continuous time diffusion. It is shown that these bounds tend to the unique Black–Scholes–Merton option price. This result is extended to equity options by assuming a linear CAPM-type relationship between index and equity returns. Content Type Journal ArticlePages 99-112DOI 10.3233/RDA-140103Authors Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-mail: michael.oancea@business.uconn.eduStylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: perrakis@jmsb.concordia.ca Content Type Journal ArticleContent Type Journal ArticlePages 99-112DOI 10.3233/RDA-140103Authors Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-mail: michael.oancea@business.uconn.eduStylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: perrakis@jmsb.concordia.ca Authors Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-mail: michael.oancea@business.uconn.eduStylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: perrakis@jmsb.concordia.ca Ioan Mihai Oancea, University of Connecticut School of Business, Stamford, CT, USA. E-mail: michael.oancea@business.uconn.eduStylianos Perrakis, John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: perrakis@jmsb.concordia.ca Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Volume Volume 5 Journal Issue Volume 5, Number 2-3 / 2014 Journal Risk and Decision AnalysisOnline ISSN 1875-9173Print ISSN 1569-7371 Journal Risk and Decision AnalysisJournal Risk and Decision AnalysisRisk and Decision AnalysisOnline ISSN 1875-9173Online ISSN 1875-9173Print ISSN 1569-7371Print ISSN 1569-7371 Journal Volume Volume 5 Journal Volume Volume 5Journal Volume Volume 5 Journal Issue Volume 5, Number 2-3 / 2014 Journal Issue Volume 5, Number 2-3 / 2014Journal Issue Volume 5, Number 2-3 / 2014Volume 5, Number 2-3 / 2014

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