Optimal positioning in derivative securities

We consider a simple single period economy in which agents invest so as to maximize expected utility of terminal wealth. We assume the existence of three asset classes, namely a riskless asset (the bond), a single risky asset (the stock), and European options of all strikes (derivatives). In this setting, the inability to trade continuously potentially induces investment in all three asset classes. We consider both a partial equilibrium where all asset prices are initially given, and a more general equilibrium where all asset prices are endogenously determined. By restricting investor beliefs and preferences in each case, we solve for the optimal position for each investor in the three asset classes. We find that in partial or general equilibrium, heterogeneity in preferences or beliefs induces investors to hold derivatives individually, even though derivatives are not held in aggregate.