碳金融市场下基于模糊测度和Choquet积分的碳期权估值

Carbon Option Pricing based on Fuzzy Measure and Choquet Integral in Carbon Financial Market

基于投资者对投资财富和风险的偏好研究碳期权定价模型。运用λ-可加模糊测度表示投资者对碳期权价值模糊度量的差异性,借助Choquet期望积分构建投资者的期望收益效用函数;根据投资财富效用最大化推导无约束条件下碳期权的最优价;结合现实约束条件,构建投资财富效用最大化下的碳期权定价模型;通过数值计算分析效用函数、模糊参数和现实约束对碳期权定价的影响。研究结果表明:效用函数的选择会体现投资者对碳期权投资风险态度的变化,模糊测度参数的取值能够反映碳期权投资者个体的主观情绪和市场信息获取程度,现实约束会迫使碳期权投资者放弃部分投资隐含价值。

Based on the investor’s preference for investment wealth and risk,the carbon emission option pricing model is studied.First of all,the-additive fuzzy measure is used to represent the difference of investor’s fuzzy measure of carbon emission option value. The expect receipts utility function of investors is constructed by Choquet expectation integral. Secondly,according to the maximization of investment wealth utility,the optimal price of carbon option is derived under the condition of no constraint. Thirdly,combining the realistic constraints,the pricing model of the carbon emission option is constructed based on the maximization of investment wealth utility. Finally,the impact of utility function,fuzzy parameters and realistic constraints on the pricing of carbon emission option is analyzed by numerical calculation. The results show that the choice of utility function will reflect the change of investors’ attitudes towards carbon option investment risk. The value of fuzzy measure parameters can reflect the subjective sentiment of individual investors and the degree of market information acquisition. Realistic constraints will force carbon option investors to abandon part of the implicit value of investment.