Analytically Pricing Variance Swaps Under the Hawkes Jump‐Diffusion Process With Liquidity Risks
将自激霍克斯过程纳入随机流动性风险模型，推导出离散抽样方差互换的闭式定价公式，并证明其收敛于连续抽样情形，数值结果揭示跳跃聚集对执行价格的显著影响。
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.