On the Heston Model with Stochastic Interest Rates

We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these approximations we can prescibe a non-zero correlation structure between all underlying processes. The affine approximate models admit pricing basic derivative products by Fourier techniques [Carr,Madan-1999; Fang,Oosterlee-2008], and can therefore be used for fast calibration of the hybrid model