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假设项目期权标的资产服从几何均值回复过程,利用效用无差别定价原理,对非完备市场条件下的企业项目期权进行定价。得到了非完备市场下项目期权的的价格所满足的微分方程,即自由边界的二阶非线性常微分方程,并且对项目期权价格关于相应的参数进行了比较静态分析。结果表明项目期权的价格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。特别地,随着均值回复速度的增加,项目期权的价格呈现出先增大后减小的趋势。
Assuming that the underlying asset of the project option obeys the process of geometric mean recovery, the utility pricing method is used to price the enterprise project option under the incomplete market condition. The differential equation satisfied by the price of the project option under the incomplete market is obtained, ie, the second order nonlinear ordinary differential equation with free boundary and the comparative static analysis of the option price with respect to the corresponding parameters. The result shows that the price of the project option will decrease with the increase of the risk aversion coefficient, increase with the increase of the correlation coefficient and increase with the increase of the underlying asset volatility. Especially, as the average response speed increases, the price of the project option shows a trend of first increasing and then decreasing.