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Calibration of the Heston stochastic local volatility model: A finite volume scheme

Author

Listed:
  • Bernd Engelmann

    (Ho Chi Minh City Open University, 35-37 Ho Hao Hon, Dist 1, Ho Chi Minh City, Vietnam)

  • Frank Koster

    (EnBW Trading GmbH, Durlacher Allee 93, D-76131 Karlsruhe, Germany)

  • Daniel Oeltz

    (Fraunhofer-Institut SCAI, Schloss Birlinghoven, D-53757 Sankt Augustin, Germany)

Abstract

The two most popular equity and FX derivatives pricing models in banking practice are the local volatility model and the Heston model. While the former has the appealing property that it can be calibrated exactly to any given set of arbitrage free European vanilla option prices, the latter delivers more realistic smile dynamics. In this paper, we combine both modeling approaches to the Heston stochastic local volatility model. We build upon a theoretical framework that has been already developed and focus on the numerical model calibration which requires special care in the treatment of mixed derivatives and in cases where the Feller condition is not met in the Heston model leading to a singular transition density at zero volatility. We propose a finite volume scheme to calibrate the model after a suitable transformation of the model equation and demonstrate its accuracy in numerical test cases using real market data.

Suggested Citation

  • Bernd Engelmann & Frank Koster & Daniel Oeltz, 2021. "Calibration of the Heston stochastic local volatility model: A finite volume scheme," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-22, March.
    • Handle: RePEc:wsi:ijfexx:v:08:y:2021:i:01:n:s2424786320500486
    DOI: 10.1142/S2424786320500486
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    Citations

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    Cited by:

    1. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
    2. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing European options under a hybrid stochastic volatility and interest rate model with a general correlation structure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 951-967, July.
    3. Chen Zhang & Giovanni Amici & Marco Morandotti, 2024. "Calibrating the Heston Model with Deep Differential Networks," Papers 2407.15536, arXiv.org.

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