Affiliations: University of Connecticut School of Business, Stamford, CT, USA. E-mail: [email protected] | John Molson School of Business, Concordia University, Montreal, QC, Canada. E-mail: [email protected]
Note: [] Address for correspondence: Stylianos Perrakis, RBC Distinguished Professor of Financial Derivatives, John Molson School of Business, Concordia University, 1455 de Maisonneuve Blvd. W, Montreal, QC H3G 1M8, Canada. Tel.: +1 514 848 2424, ext. 2963; Fax: +1 514 848 4500; E-mail: [email protected]
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.
