A New Analytical Approach for Pricing Variance and Volatility Swaps: Incorporating Liquidity and Self‐Exciting Jumps
提出一个包含自激跳跃和流动性风险的模型，用于定价方差和波动率互换，并利用布伦特原油期货数据校准参数，验证了跳跃聚集现象。
ABSTRACT Our investigation focuses on the valuation of variance and volatility swaps by incorporating both clustered jump behaviors and liquidity‐related risk factors. The proposed modeling framework characterizes stock price movements using a jump‐diffusion process, where Hawkes processes govern the jump component in the absence of liquidity effects. Stochastic liquidity is further integrated through a discount factor that modifies the underlying asset value. To preserve model generality, we introduce a complete correlation framework across all Brownian motions involved. A change of measure is applied to express the dynamics under a risk‐neutral pricing measure. Subsequently, the forward characteristic function associated with the log‐price is expressed analytically, enabling the derivation of closed‐form swap valuation formulae. Using daily data from the Brent crude oil futures continuous contract, we calibrate relevant model parameters, providing empirical evidence supporting jump clustering. Numerical implementation of the formulae further offers insights into their sensitivity to variations in model parameters.