Valuations of generalized variance swaps under the jump–diffusion model with stochastic liquidity risk

Abstract

This paper focuses on the pricing problem of generalized variance swaps with jump risk in the underlying asset price under a stochastic liquidity model. We obtain a pricing formula of generalized variance swap in a jump–diffusion model with stochastic liquidity risk by the joint moment generating function (MGF) generated by solving the partial integral differential equation (PIDE). Using asymptotic analysis, we also demonstrate that as the sampling interval approaches zero, the pricing formula of discretely sampled generalized variance swap tends to be that of continuously sampled generalized variance swap. Finally, to verify the feasibility of the pricing formula of the generalized variance swap presented in this paper, we conduct some numerical experiments, including a comparison with the results of Monte Carlo (MC) simulation, the impact of various model parameters on the delivery prices of generalized variance swaps, and empirical research using actual market data.