On the Heston Model with Stochastic Interest Rates

Grzelak, Lech A.; Oosterlee, Cornelis W.

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On the Heston Model with Stochastic Interest Rates

SIAM Journal on Financial Mathematics 2, 255–286, 2011

25 Pages Posted: 15 Apr 2009 Last revised: 6 Aug 2014

See all articles by Lech A. Grzelak

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: July 30, 2010

Abstract

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.

Keywords: Heston-Hull-White, Heston-Cox-Ingersoll-Ross, equity-interest rate hybrid products, affine jump diffusion processes

JEL Classification: G12, G13

Suggested Citation: Suggested Citation

Grzelak, Lech Aleksander and Oosterlee, Cornelis W., On the Heston Model with Stochastic Interest Rates (July 30, 2010). SIAM Journal on Financial Mathematics 2, 255–286, 2011, Available at SSRN: https://ssrn.com/abstract=1382902