Calibration of the double Heston model and an analytical formula in pricing American put option

This paper proposes a novel approach to pricing of American put option under double Heston model. We develop an analytical solution to the double Heston partial differential equation (double Heston PDE) using the equivalent European put option price and standard portfolio-consumption model. Then through the affine form of the model and Fourier transform method, we evaluate the American put option price. Finally, we calibrate the option prices resulting from double Heston model to a set of observed index options by employing Genetic optimization algorithm. A detailed numerical study illustrates the efficiency of the proposed method.