A probabilistic approach for the valuation of variance swaps under stochastic volatility with jump clustering and regime switching

Abstract

The effects of stochastic volatility, jump clustering, and regime switching are considered when pricing variance swaps. This study established a two-stage procedure that simplifies the derivation by first isolating the regime switching from other stochastic sources. Based on this, a novel probabilistic approach was employed, leading to pricing formulas with time-dependent and regime-switching parameters. The formulated solutions were easy to implement and differed from most existing results of variance swap pricing, where Fourier inversion or fast Fourier transform must be performed to obtain the final results, since they are completely analytical without involving integrations. The numerical results indicate that jump clustering and regime switching have a significant influence on variance swap prices.