Grzelak, Lech and Oosterlee, Kees (2009): On The Heston Model with Stochastic Interest Rates.
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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.
Item Type: | MPRA Paper |
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Original Title: | On The Heston Model with Stochastic Interest Rates |
English Title: | On The Heston Model with Stochastic Interest Rates |
Language: | English |
Keywords: | Heston-Hull-White; Heston-Cox-Ingersoll-Ross; equity-interest 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: | 28 Sep 2019 20:48 |
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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/20620 |
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