Accelerated implementation of the ADI schemes for the Heston model with stochastic correlation

Abstract

This work deals with the numerical solution of the extended Heston model with stochastic correlation using the Alternating Direction Implicit (ADI) type schemes. By imposing stochastic correlation driven by a stochastic process between the underlying asset and the stochastic volatility in the Heston model, we obtain three-dimensional equation with the mixed derivative terms. We thus choose the ADI type schemes to solve this problem, and investigate the effective implementation in matrix form. Our numerical results demonstrate the achieved acceleration using the proposed implementation, where several classical ADI schemes are considered and compared.