Consumption-utility Based Pricing Of Receipts Produced By A Non-traded Claim

This paper puts forward a approach of consumption-utility based pricing European options in complete and incomplete markets. In incomplete market assumption we come to the conclusion different from the traditional one as the existence of idiosyncratic risk and the trader's precautionary motive. In traditional real option theory, the increase of volatility of project value would raise the investment trigger and the implied value of real option. Nevertheless, this result is merely adapted to assumption that the problem is characterized by complete market or risk neutral agent, which is not easily found in reality. This paper brings in utility function, takes the maximum of expected utility as main object and adopts dynamic programming to achieve the optimal strategy of investment and consumption. During the process above we could discover that the optimal investment level and value of real option are influenced by precautionary saving motive. This influence largely depends on intensity of precautionary saving motive, which within this paper is measured by the coefficient of risk aversion. 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. Futhermore, we find the influence of investment trigger caused by movement of risk aversion coefficient in lump-sum assumption is more evident than the one in cash-flow. In lump-sum surroundings, Increase of volatility of project value return even would incur decline of the investment trigger when risk aversion coefficient is sufficiently large. Lastly, the conclusions of classical Black-Scholes models are recovered even for a general utility function.