Analytically Pricing Variance Swaps Under the Hawkes Jump‐Diffusion Process With Liquidity Risks

ABSTRACT We investigate variance swap pricing by incorporating a self‐exciting Hawkes process into a stochastic liquidity risk model. Within this framework, we derive closed‐form pricing formulas for discretely sampled variance swaps using two different methods. Through asymptotic analysis, we demonstrate that the discretely sampled pricing formulas converge to their continuously sampled counterparts as the sampling interval approaches zero. Numerical results further highlight the significant impact of jump clustering on the strike prices of variance swaps.