Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

In this paper, we investigate the effects of imposing stochastic interest rate driven by the Cox-Ingersoll-Ross process along with the Heston stochastic volatility model for pricing variance swaps with discrete sampling times. A dimension reduction mechanism based on the framework of Little and Pant (2001) is applied which later reduces to solving two three-dimensional partial differential equations. A semi-closed form solution to the fair delivery price of a variance swap is obtained via the derivation of characteristic functions. Practical implementation of this hybrid model is demonstrated through numerical simulations.