基础资产不可交易条件下欧式期权的消费效用无差别定价

Consumption Utility-based Indifference Pricing of European Options on Nontradable Underlying Assets

基于消费效用无差别准则,讨论非完备市场下欧式期权定价问题.在完备市场下,验证了关于一般效用函数的效用无差别定价等同于经典Black-Scholes期权定价.在非完备市场下,通过假设投资者具有CARA效用,发现期权消费效用无差别价格会随期权标的资产价格波动率增加或期限延长反而降低.风险态度只有与期权非系统风险相结合才对期权消费效用无差别价格产生影响,期权的非系统风险越小,风险态度对期权效用无差别价格影响越弱,当非系统风险为零时,投资者风险态度不对期权价格产生影响.

This paper studied the pricing problem of European option under an incomplete market on the basis of consumption utility indifference.The conclusions of Black-Scholes models were recovered even for a general utility function.In contrast to complete markets,it is found that the utility indifference price for CARA utility may decrease if the volatility of the underlying asset or the lifetime of the option increases under the incomplete market.The risk attitude of an investor has effects on option prices only if there is idiosyncratic risk exposed in the option.The smaller the idiosyncratic risk exposed in the option,the weaker the effect of the risk attitude on the consumption utility indifference price.Especially,if there is no idiosyncratic risk exposed in the option,the risk attitude will make no impact on option prices.