Switch Corridor方差互换定价的蒙特卡罗加速算法

Monte Carlo Acceleration Algorithm of Pricing Switch Corridor Variance Swap

摘要:

主要研究为对冲跨市场波动率风险而开发的双标的资产的新型方差产品——Switch Corridor方差互换的定价问题。该产品由瑞士信贷（Credit Suisse）于2012年率先推出，逐渐成为了结构性产品市场上最受欢迎的新产品系列之一。使用控制变量Monte Carlo方法研究了双Heston随机波动率模型下Switch Corridor方差互换的定价问题，基于仿射结构理论，得到辅助标的过程下方差产品价格的解析解，构造了问题求解的高效控制变量。进一步地，考察了不同辅助过程波动率的选取对加速效果的影响。通过数值实验可以证明，基于动态波动率选取的辅助过程起到了很好的加速效果。该算法亦可方便地解决其他随机波动率模型下高维方差产品的计算问题。

Abstract:

The pricing problem of Switch Corridor variance swap， a new variance product based on two underlying assets， is studied in this paper. This product was first launched for hedging cross-market volatility risk by Credit Suisse in 2012 and has gradually become one of the most popular new product series in the structured financial derivative market. The control variate Monte Carlo method is used to solve the problem in double Heston stochastic volatility models. Based on the affine structure theory， the closed-form solution in an auxiliary process was obtained， which constructs an efficient control variate. Further， three different kinds of volatilities of the auxiliary were adopted. By means of numerical experiments， the solution in the process with dynamic volatility is proved to have an extraordinary effect on acceleration. The algorithm can also be used to solve the calculation problem of other high-dimensional variance products in various stochastic volatility models.