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

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.