Jump-Diffusion Volatility Models for Variance Swaps : An Empirical Performance Analysis

This paper studies a class of tractable jump-diffusion models,including stochastic volatility models with self-exciting jumpsfor stock returns and variance processes. We employ the Markovchain Monte Carlo (MCMC) method to implement model estimation, andinvestigate the performance of all models in fitting the dynamicsof stock returns and capturing the term structure of variance swaprates. It is evident that the stochastic volatility models,equipped with self-exciting jumps in the spot variance andlinearly-dependent jumps in the central-tendency variance, canproduce consistent model estimates, aptly explain the stylizedfacts in variance swaps, and boost pricing performance. Moreover,our empirical results show that large self-exciting jumps in thespot variance, as an independent risk source, facilitate termstructure modelling for variance swaps, whilst thecentral-tendency variance may jump with small sizes. Both types ofjumps occur infrequently, and are more related to market turmoilsover the period from 2008 to 2021