Articlegreen2011

On the Heston Model with Stochastic Interest Rates

Lech Aleksander Grzelak · Cornelis W. Oosterlee

248 citations0/0 files storedSIAM Journal on Financial Mathematics

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

We discuss the Heston model [Rev. Financ. Stud., 6 (1993), pp. 327–343] with stochastic interest rates driven by Hull–White (HW) [J. Derivatives, 4 (1996), pp. 26–36] or Cox–Ingersoll–Ross (CIR) [Econometrica, 53 (1985), pp. 385–407] processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these approximations we can prescribe a nonzero correlation structure between all underlying processes. The affine approximate models admit pricing basic derivative products by Fourier techniques [P. P. Carr and D. B. Madan, J. Comput. Finance, 2 (1999), pp. 61–73, F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826–848] and can therefore be used for fast calibration of the hybrid model.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 1977An equilibrium characterization of the term structure 2003Stochastic Differential Equations 2000Transform Analysis and Asset Pricing for Affine Jump-diffusions 1999Option valuation using the fast Fourier transform 2001Interest Rate Models Theory and Practice

Cited by

2014Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework 2017A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps 2012EFFICIENT PRICING AND RELIABLE CALIBRATION IN THE HESTON MODEL 2017A closed-form pricing formula for European options under the Heston model with stochastic interest rate 2011On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates 2013Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates

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