方差衍生产品定价与控制变量蒙特卡罗方法

Variance Derivatives Pricing and Control Variate Monte Carlo Method

建立了方差互换金融衍生产品的定价模型,基于控制变量技巧,对随机波动率情形下的一类方差互换产品的定价问题,提出了一种有效的蒙特卡罗计算方法.通过进一步的理论分析和高效率控制变量的选取,大大减小了模拟误差,提高了计算效率.最后,对数值结果进行了分析,并考察了影响方差互换产品价格的因素.该计算方法可为其他方差互换衍生产品,如Corridor方差互换、Gamma方差互换和Conditional方差互换等产品以及其他多因子模型假设下的衍生产品定价提供有效思路.

The paper presents an efficient Monte Carlo method on the basis of the Control Variate technique for valuation of the Variance Swap derivatives under the stochastic volatility assumption. The result shows that the method can reduce variance efficiently and improve precision obviously by choosing an efficient control variate testified with the computation results. Finally, a study is also made of the factors affecting the price of the Variance Swap. The method can also be applied to the other valuation of Variance Swaps, such as Corridor Variance Swap, Gamma Variance Swap, Conditional Variance Swap and other products with multifactor models.