On The Heston Model with Stochastic Interest Rates

Lech Grzelak and Cornelis Oosterlee

MPRA Paper from University Library of Munich, Germany

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. A so-called volatility compensator is defined which guarantees that the Heston hybrid model with a non-zero correlation between the equity and interest rate processes is properly defined. Two different approximations of the hybrid models are presented in order to obtain the characteristic functions. These approximations admit pricing basic derivative products with Fourier techniques [Carr,Madan-1999; Fang,Oosterlee-2008], and can therefore be used for fast calibration of the hybrid model. The effect of the approximations on the instantaneous correlations and the influence of the correlation between stock and interest rate on the implied volatilities are also discussed.

Keywords: Heston-Hull-White; Heston-Cox-Ingersoll-Ross; equity-interest rate hybrid products; stochastic volatility; affine jump diffusion processes. (search for similar items in EconPapers)
JEL-codes: F3 G1 G13 (search for similar items in EconPapers)
Date: 2009-02-17, Revised 2010-01-18
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (49)

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https://mpra.ub.uni-muenchen.de/24174/1/MPRA_paper_24174.pdf revised version (application/pdf)

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