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This paper considers the case of pricing discretely-sampled variance swapsunder the class of equity-interest rate hybridization. Our modeling frameworkconsists of the equity which follows the dynamics of the Heston stochasticvolatility model, and the stochastic interest rate is driven by theCox-Ingersoll-Ross (CIR) process with full correlation structure imposed amongthe state variables. This full correlation structure possess the limitation tohave fully analytical pricing formula for hybrid models of variance swaps, dueto the non-affinity property embedded in the model itself. We address thisissue by obtaining an efficient semi-closed form pricing formula of varianceswaps for an approximation of the hybrid model via the derivation ofcharacteristic functions. Subsequently, we implement numerical experiments toevaluate the accuracy of our pricing formula. Our findings confirmed that theimpact of the correlation between the underlying and the interest rate issignificant for pricing discretely-sampled variance swaps.

Pricing variance swaps with stochastic volatility and stochastic interest rate under full correlation structure