Two-factor Heston model equipped with regime-switching: American option pricing and model calibration by Levenberg-Marquardt optimization algorithm

Abstract

In this paper, we consider the pricing of American options under a regime-switching double Heston model, such that the interest rate and mean-reversion level parameters in both stochastic volatility models shift in various states. We develop a semi-analytical formula for double Heston partial differential equation by using the equivalent European put option price and standard portfolio-consumption model. Then through the moment-generating function of this particular model, the American put option price is evaluated. We employ the Levenberg-Marquardt optimization method to calibrate the regime-switching double Heston model. Numerical experiments have also been performed to demonstrate the accuracy of the proposed formula and the performance of regime change mechanism on option pricing. Ultimately, through an experimental application, we indicate the proposed model is premier to the double Heston model, which illustrates the importance of considering regime-switching factor. 2022 International Association for Mathematics and Computers in Simulation (IMACS)