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Numerical Simulation of the Heston Model under Stochastic Correlation

Author

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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)

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.

Suggested Citation

  • Long Teng & Matthias Ehrhardt & Michael Günther, 2017. "Numerical Simulation of the Heston Model under Stochastic Correlation," IJFS, MDPI, vol. 6(1), pages 1-16, December.
    • Handle: RePEc:gam:jijfss:v:6:y:2017:i:1:p:3-:d:124327
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    References listed on IDEAS

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    1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
    4. Jun Ma, 2009. "Pricing Foreign Equity Options with Stochastic Correlation and Volatility," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 303-327, November.
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