  In this paper, we consider the Heston-CIR model with L\'{e}vy process for
pricing in the foreign exchange (FX) market by providing a new formula that
better fits the distribution of prices. To do that, first, we study the
existence and uniqueness of the solution to this model. Second, we examine the
strong convergence of the L\'{e}vy process with stochastic domestic short
interest rates, foreign short interest rates and stochastic volatility. Then,
we apply Least Squares Monte Carlo (LSM) method for pricing American options
under our model with stochastic volatility and stochastic interest rate.
Finally, by considering real-world market data, we illustrate numerical results
for the four-factor Heston-CIR L\'{e}vy model.
