Forward-Price Processes and the Risk-Neutral Pricing of Options

This paper investigates the preference restrictions which underlie the Black-Scholes (log-normal), Brennan (normal), and Rubinstein (generalized lognormal) option pricing models. It also introduces a fourth option pricing model for assets which have negatively skewed returns. It establishes new sufficient conditions for the models to hold in a multi-asset economy. First, assuming that expectations of an asset price follow a lognormal diffusion, we derive the Black-Scholes model in an economy where the representative agent has an extended power utility function of wealth. We then establish the Brennan model assuming that expectations follow a normal diffusion in an economy where the representative agent again has an extended power utility function. Then we assume that expectations follow a displaced diffusion and derive conditions under which the Rubinstein model holds. Fi-nally we assume that an asset has a negatively skewed lognormal distribution as in the bond option model of Stapleton and Subrahmanyam (1993) and again derive conditions for risk-neutral pricing of options.