On the pricing of forward-start variance swaps with stochastic volatility and stochastic interest rate

Variance swaps have gained an immense recognition in the financial market based on the tremendous spike in its trading volume since late 1990s. Being categorized under volatility derivatives, the substance of variance swaps can be related to the vital role of volatility in making investment decisions. In this paper, the price of discretely-sampled forward-start variance swaps is evaluated using an equity-interest rate hybrid model. The modeling framework involves an extension of the Heston stochastic volatility model, which is combined with the dynamics of the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. Focus is given on the forward-start nature, identified by the starting time of the sampling period being a future date. Previous studies on variance swaps were mainly focusing on instantaneous-start variance swaps, whereas in reality, most of traded variance swap