Heterogeneity and Option Pricing

Abstract:     
We consider equilibrium option pricing in a simple two-period economy that is characterized by heterogeneity among agents. We demonstrate that an economy in which agents have constant yet heterogeneous degrees of relative risk aversion will price assets as though it has a single "pricing representative" agent who displays decreasing relative risk aversion. This result is shown to imply that the pricing kernel has fat tails and yields option prices which do not conform to the standard Black-Scholes formula. Solving for the implied volatility results in a smile pattern, typical of those seen in practice. This pattern was in fact obtained is several cases. Even though we assume a lognormal distribution of the underlying return, we obtain that heterogeneity in either risk aversion or in beliefs concerning the distribution parameters implies a non-lognormal pricing kernel with fatter tails and with "over-pricing" of out-of-the-money call and put options.

Number of Pages in PDF File: 39

JEL Classification: G13

working papers series