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.
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