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. 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.
|Date of creation:||17 Feb 2009|
|Date of revision:||18 Jan 2010|
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- Fang, Fang & Oosterlee, Kees, 2008.
"A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions,"
9319, University Library of Munich, Germany.
- Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 7700, University Library of Munich, Germany.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, vol. 49(8), pages 1071-1088, August. Full references (including those not matched with items on IDEAS)