对数效用函数理论下的可违约欧式期权定价

The Price Formulas of Default European Option Under Logarithmic Utility

完全信息下的经济学都是假定投资者知道资产的期望均值和波动率,但是现实中资产的期望均值我们往往并不知道,投资者只能根据历史数据去估计,即信息不完全.因此,投资者拥有的信息和个人偏好会影响资产的定价.本文在代理人经济模型上根据第一福利定理得到了代理人之间有不同信仰和对数效用函数情况下各自的均衡消费,进而根据资产定价一般原理给出资产的均衡价格和贴现因子,得到了资产的均衡价格不受投资者信仰的影响和贴现因子为相同信仰下的加权平均的结论,最后根据期权定价理论结合信用风险强度模型给出了公司存在违约情况下,标的资产为公司股票的可违约欧式期权的定价公式.

The economics under complete information always assumed that investors knew the assets;expected return and volatility,but in real world it is unknown to us and can but be estimated by historic data,i, e. incomplete information. So the information and personal taste Which investors owned affect the assets＇ price. On the base of the agent economic model and according to the first wel- fare theory this paper gained each equilibrium consumption , on the conditions of heterogeneous beliefs between of agents and logarithmic utility. Furthermore, according to the asset pricing theory this paper educed the assetst equilibrium price and discount factor. obtained such conclusions that the assets＇ equilibrium price is unaffected by investors＇ beliefs and the discount factor is equal to the weighted averaged of the values that in corresponding economics with homogeneous beliefs. At last,this paper gave the default European option pricing formula which underlying asset is company＇s stock, on the base of the option pricing theory and the credit risk intensity model.