Numerical Simulation of the Heston Model under Stochastic Correlation

Long Teng, Matthias Ehrhardt and Michael Günther
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Long Teng: Chair of Applied Mathematics and Numerical Analysis, Faculty of Mathematics and Natural Sciences, University of Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
Matthias Ehrhardt: Chair of Applied Mathematics and Numerical Analysis, Faculty of Mathematics and Natural Sciences, University of Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
Michael Günther: Chair of Applied Mathematics and Numerical Analysis, Faculty of Mathematics and Natural Sciences, University of Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

IJFS, 2017, vol. 6, issue 1, 1-16

Abstract: Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

Keywords: Heston model; stochastic correlation process; Ornstein-Uhlenbeck process; quadratic-exponential scheme (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2017
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