  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.
