Who buys and who sells options: The role and pricing of options in an economy with background risk

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, the demand for these contracts is not explained by differences in the shape of the 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 sell portfolio insurance, i.e., they sell options on the market portfolio, whereas investors with high background risk buy those 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. However, in an economy with given background risk, holding the forward price and hence the overall risk aversion constant, all options will be underpriced by the option pricing model if it ignores the presence of background risk.