Who Buys and Sells Options: The Role and Pricing of Options in an Economy with Background Risk

Abstract

In this paper, we derive an equilibrium in which some investors buy call/put options on the market portfolio while others sell them. Also, some investors supply and others demand forward contracts. Since investors are assumed to have similar risk-averse preferences, demand for these contracts is not explained by differences in the shape of utility functions. Rather, it is the degree to which agents face other, non-hedgeable, background risks that determines their risk-taking behavior in the model. We show that investors with low or no background risk have a concave sharing rule, i.e., they sell options on the market portfolio, whereas investors with high background risk have a convex sharing rule and buy these options. A general increase in background risk in the economy reduces the forward price of the market portfolio. Furthermore, the prices of put options rise and the prices of call options fall. Investors without background risk then react by choosing a sharing rule with higher slope and concavity.