Valuation of discretely-sampled variance swaps under correlated stochastic volatility and stochastic interest rates

In this paper, we evaluate the price of discretely-sampled variance swaps using a equity-interest rate hybrid model. Our modeling framework extends the Heston stochastic volatility model by including the Cox-Ingersoll-Ross stochastic interest rates and imposes correlation between the stochastic interest rate and volatility. It is known that one limitation of the hybrid models is that the analytical pricing formula is often unavailable due to the non-affinity property of hybrid models. An efficient semi-closed form pricing formula is derived for an approximation of the fully correlated hybrid model. Our pricing formula which involves solving two phases of three-dimensional partial differential equations is evaluated through numerical implementations to confirm its accurac