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On The Heston Model With Stochastic Correlation

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  • LONG TENG

    (Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany)

  • MATTHIAS EHRHARDT

    (Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany)

  • MICHAEL GÜNTHER

    (Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany)

Abstract

The degree of relationship between financial products and financial institutions, e.g. must be considered for pricing and hedging. Usually, for financial products modeled with the specification of a system of stochastic differential equations, the relationship is represented by correlated Brownian motions (BMs). For example, the BM of the asset price and the BM of the stochastic volatility in the Heston model correlates with a deterministic constant. However, market observations clearly indicate that financial quantities are correlated in a strongly nonlinear way, correlation behaves even stochastically and unpredictably. In this work, we extend the Heston model by imposing a stochastic correlation given by the Ornstein–Uhlenbeck and the Jacobi processes. By approximating nonaffine terms, we find the characteristic function in a closed-form which can be used for pricing purposes. Our numerical results and experiment on calibration to market data validate that incorporating stochastic correlations improves the performance of the Heston model.

Suggested Citation

  • Long Teng & Matthias Ehrhardt & Michael Günther, 2016. "On The Heston Model With Stochastic Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-25, September.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:06:n:s0219024916500333
    DOI: 10.1142/S0219024916500333
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    References listed on IDEAS

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    Cited by:

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    2. Bianca Reichert & Adriano Mendon a Souza, 2022. "Can the Heston Model Forecast Energy Generation? A Systematic Literature Review," International Journal of Energy Economics and Policy, Econjournals, vol. 12(1), pages 289-295.
    3. Kim, See-Woo & Kim, Jeong-Hoon, 2018. "Analytic solutions for variance swaps with double-mean-reverting volatility," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 130-144.
    4. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.
    5. Ah-Reum Han & Jeong-Hoon Kim & See-Woo Kim, 2021. "Variance Swaps with Deterministic and Stochastic Correlations," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1059-1092, April.

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