American option pricing under double Heston stochastic volatility model: simulation and strong convergence analysis

In this work, we investigate the double Heston model dynamics which is defined by two independent variance processes with non-Lipschitz diffusions. Next, it is analysed the strong convergence of the volatility processes of the double Heston model. Then, we examine the LSM algorithm to determine the American style option price in the double Heston model. Besides, by performing the antithetic simulation in the original LSM algorithm, we aim to accelerate the algorithm. The accuracy and speed of two algorithms are studied and at last, by some numerical results illustrate the accuracy of the proposed algorithms and examine the effect of the different parameters of the model on the value of the option.