基础资产不可交易的欧式期权消费效用无差别定价

his paper puts forward a new approach of consumption-utility based pricing European options in complete and incomplete markets. The conclusions of Black-Scholes models are recovered even for a general utility function. In incomplete market model, we obtain numerically consumption-utility based price of European options for CARA utility. In contrast to the increase of the European option price with the time to maturity in complete markets, the option price also depends on investor’s attitude toward risk and especially, if the risk aversion coefficient gets large enough, the consumption-utility indifference price may decrease with the time to maturity. It is shown that the change of option price results from the risk attitude of an investor only if there is idiosyncratic risk exposed in the option. Concretely speaking, the stronger the correlation between the tradable asset and the underlying asset, the smaller the idiosyncratic risk exposed in the option and thus, the weaker the effect of the risk attitude on the consumption-utility indifference price. Especially, if the tradable asset is completely correlated to the underlying asset, there is no idiosyncratic risk exposed in the option and consequently, the risk attitude will make no impact on option price. In addition, the results also explain that, if keep other conditions unchanged, the option, which underlying asset is negatively correlated to the tradable asset, is more valuable than the option, which underlying asset is positively correlated to the tradable asset.