Variance swaps with mean reversion and multi-factor variance

This paper proposes a novel model for the valuation of variance swaps that incorporates a multi-factor stochastic spot variance and a multi-factor stochastic long-term variance, while allowing mean reversion in the asset price and a co-jump structure in the model. We propose a general analytical approach for pricing discretely monitored variance swaps via a moment-based method and confirm its accuracy and efficiency using Monte Carlo simulations. Our empirical results indicate that the model with a three-factor spot variance and a one-factor long-term variance significantly outperforms other nested models. The incorporation of multiple factors in our model is essential not only for fitting market data, but also for reconciling the term structure of variance swaps.