Stochastic Dominance and Option Pricing in Discrete and Continuous Time: an Alternative Paradigm

This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time 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, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrageand equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jumpdiffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.