资产跳跃下CM策略多期收入保证价格模拟——基于条件蒙特卡罗方法

Simulation of value of CM strategy multi-period return guarantee under asset jump——Based on the conditional Monte Carlo method

恒定混合策略(CM策略)多期收入保证价格是保本基金发行方采取设置止损的CM策略作为投资策略时收取保本费的理论依据,其中标的资产由复合泊松过程和维纳过程共同驱动,这一定价问题内嵌奇异期权,蒙特卡罗模拟方法擅长处理这种高维数量金融问题.基于风险中性测度推导出多期收入保证价格的现值表达式,用条件蒙特卡罗推导出这一现值表达式的模拟公式.在给定参数下分别用普通蒙特卡罗和条件蒙特卡罗计算CM策略多期收入保证价格的数值解,结果显示两种蒙特卡罗方法均能有效计算其数值解,之后通过给定显著性水平下的置信区间长度评价两种方法的精确度,结果显示条件蒙特卡罗比普通蒙特卡罗有很大改进.接着运用条件蒙特卡罗模拟研究多期收入保证价格对不同参数范围的变化情况.

Value of constant mix strategy （CM strategy） multi-period return guar- antee is theoretical basis of charging by the issuers who use CM strategy set stop-loss to manage a principal guaranteed fund. The underlying asset is driven by compound Poisson process and Wiener process. This pricing problem embeds exotic options. Monte Carlo simulation is good at dealing with such a high dimensional quantitative financial problems. We derive the expression of the present value of CM strategy multi-period re- turn guarantee that based on risk-neutral measurement. Then we use conditional Monte Carlo simulation to derive the simulation formula of this present value. Numerical solu- tions of value of CM strategy multi-period return guarantee were calculated under given parameters by ordinary Monte Carlo and conditional Monte Carlo. Results show two Monte Carlo methods can calculate the numerical solution effectively. Then we appraise the accuracy of the two methods through the length of the confidence interval under a given level of significance. Results show conditional Monte Carlo is better than ordinary Monte Carlo. Then we use conditional Monte Carlo simulation to analyze value of CM strategy multi-period return guarantee on the different parameters range.