Risk Sharing in a Dynamic CAPM with Endogenous Option Prices∗

This paper investigates a dynamic CAPM in which investors may trade in put option contracts which are zero in net supply. In each period, stock and option prices are endogenously and simultaneously determined by market clearing in the respective markets. We investigate how these endogenously formed option prices impact on prices and portfolio allocations. The introduction of a put-option market will decrease systematic risk but increase the price of risk in a financial market. Investors with mean-variance preference will generally hold portfolios which consist of the primary asset and the option contract, thereby increasing the risk in their portfolios in exchange for higher return. While the introduction of an option market will not affect the aggregate wealth process of a financial market, it is shown that short selling in option contracts will increase the volatility of individual wealth processes. Investors with erroneous beliefs may be better off not trading in put option contracts.