Grzelak, Lech and Oosterlee, Kees (2009): On The Heston Model with Stochastic Interest Rates.
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Abstract
We discuss the Heston [Heston1993] model with stochastic interest rates driven by HullWhite [Hull,White1996] (HW) or CoxIngersollRoss [Cox, et al.1985] (CIR) processes. A socalled volatility compensator is defined which guarantees that the Heston hybrid model with a nonzero 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,Madan1999; Fang,Oosterlee2008], 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.
Item Type:  MPRA Paper 

Original Title:  On The Heston Model with Stochastic Interest Rates 
English Title:  On The Heston Model with Stochastic Interest Rates 
Language:  English 
Keywords:  HestonHullWhite; HestonCoxIngersollRoss; equityinterest rate hybrid products; stochastic volatility; affine jump diffusion processes. 
Subjects:  G  Financial Economics > G1  General Financial Markets F  International Economics > F3  International Finance G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  20620 
Depositing User:  Lech A. Grzelak 
Date Deposited:  12. Feb 2010 03:48 
Last Modified:  14. Feb 2013 17:22 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/20620 
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