A closed-form pricing formula for variance swaps under a stochastic volatility model with a stochastic mean-reversion level

In this paper, we consider the valuation of variance swaps under a modified Heston model with a stochastic mean-reversion level, as a time-dependent mean reversion level for the variance of the Heston volatility model could provide better fit into the term structure of implied volatility and variance swap curve (Byelkina and Levin, in: Sixth World Congress of the Bachelier Finance Society, Toronto 2010; Forde and Jacquier in Appl Math Financ 17:241-259). We present a closed-form pricing formula for discretely sampled variance swaps based on the dimensional reduction technique. The validity of the newly derived formula is demonstrated through the comparison with the Monte Carlo simulation. The influence of introducing the stochastic mean-reversion level on variance swap prices is further investigated with numerical experiments.