Numerical methods and software
Numerical methods and software
Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
Application of the Fast Gauss Transform to Option Pricing
Management Science
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
SIAM Journal on Scientific Computing
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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.