非完备市场中项目期权的消费效用无差别定价

Consumption-utility indifference pricing for the project option to invest in an incomplete market

基于消费效用最大化的效用无差别定价原理,本文对非完备市场条件下的企业项目期权进行定价.假设企业家具有指数效用函数,得到了项目期权的定价方程.即带自由边界的二阶非线性常微分方程;通过数值模拟发现,项目期权执行的最优触发值和期权价值会随着风险厌恶系数的增加而减小,随着相关系数的增加而增大,随着项目标的资产波动率的增加而增大.

Based on the consumption-utility indifference pricing principle, we study the pricing problem of an entrepreneur＇s option to invest in a project in an incomplete market. Assuming that the entrepreneur has exponential utility function, the pricing equation of the option is derived, which is a second order nonlinear ordinary differential equation with free boundary conditions. Through numerical simulations, we find that the optimal investment threshold and option value are decreasing in risk aversion coefficient and increasing in the correlation between assets and the volatility of the project.