Modeling of Variance Swap and Improved Control Variate for Monte Carlo Method

This study proposes the partial differential equation pricing model for the variance swap derivatives under the stochastic volatility structure. Control variate technique is applied to valuation of the derivatives, based on the closed form solutions in a simpler model. Then with the analysis of the moments for the underlying processes, a method to choose high efficient control variate for Monte Carlo simulation is provided. The computation results show that our method can reduce variance efficiently, and are in line with the theoretical analysis. The method in the paper can also be extended to the valuation of other types of variance swaps, such as Corridor Variance Swap, Gamma Variance Swap, Conditional Variance Swap and other products with multi-factor models.