The influence of heterogeneous preferences on asset prices in an incomplete market model

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the construction of a riskless hedge-portfolio to valuate the option is unfeasible and therefore the pricing of the assets becomes a simultaneous valuation problem, nonlinearly depending on the preferences of the agents. First, the case of homogeneous agents (or, equivalently, of a representative agent) is studied. By means of numerical analysis, it can be found that individual preferences have a major impact on the price relation of the assets, including the price of the option. This stays in contrast to the Black-Scholes analysis, where the option is a redundant asset. A unique price relation exists and no trading takes place. In the case of heterogeneous agents the price relation of the assets crucially depends on the span of heterogeneity of the preferences. Now, trading takes place. The more risk averse agents buy the bond and sell the share and the option, whereas the less risk averse agents buy the option and the share and sell the riskless bond. More surprisingly we find that the representative asset-pricing-model overprices the riskless bond and underprices the option in relation to our model of heterogeneous agents.