This study focuses on the pricing of the variance swap in the financial market where the stochastic interest rate and the volatility of the stock are  driven by Cox-Ingersoll-Ross model and Heston model with simultaneous L\'{e}vy jumps , respectively. After transforming the physical probability measure to the forward measure , we obtain a closed-form solution of the related moment-generating function having the martingale property and the affine structure . Moreover, we get the fair delivery price of the variance swap via the derivation of the moment-generating function under some mild conditions . Finally,  some numerical examples are given to show that the values of variance swaps not only depend on the stochastic interest rates but also are higher in the presence of jump risks.
This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous L\'{e}vy jumps . By using the equilibrium framework , we obtain the pricing kernel and the equivalent martingale measure . Moreover, under the forward measure instead of the risk neural measure, we give the closed-form solution for the fair delivery price of the discretely sampled variance swap by employing the joint moment generating function of the underlying processes . Finally, we provide some numerical examples to depict that the values of variance swaps not only depend on the stochastic interest rates but also increase in the presence of jump risks.
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