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Efficient Pricing And Reliable Calibration In The Heston Model

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  • SERGEI LEVENDORSKIĬ

    (Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK)

Abstract

We suggest a general scheme for improvement of FT-pricing formulas for European options and give efficient recommendations for the choice of the parameters of the numerical scheme, which allow for very accurate and fast calculations. The efficiency of the method stems from the properties of functions analytical in a strip, which were introduced to finance by Feng and Linetsky (2008). We demonstrate that an indiscriminate choice of parameters of a numerical scheme leads to an inaccurate pricing and calibration. As applications, we consider the Heston model and its generalization. For many parameter sets documented in empirical studies of financial markets, relative accuracy better than 0.01% can be achieved by summation of less than 10-20 terms even in the situations in which the standard approach requires more than 200. In some cases, the one-term formula produces an error of several percent, and the summation of two terms — less than 0.5%. Typically, 10 terms and fewer suffice to achieve the error tolerance of several percent and smaller.

Suggested Citation

  • Sergei Levendorskiĭ, 2012. "Efficient Pricing And Reliable Calibration In The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-44.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:07:n:s0219024912500501
    DOI: 10.1142/S0219024912500501
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    References listed on IDEAS

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
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    Cited by:

    1. Svetlana Boyarchenko & Sergei Levendorskiä¬ & J. Lars Kyrkby & Zhenyu Cui, 2021. "Sinh-Acceleration For B-Spline Projection With Option Pricing Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(08), pages 1-50, December.
    2. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of expectations of functions of a stable L\'evy process and its extremum," Papers 2209.12349, arXiv.org.
    3. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Simulation of a L\'evy process, its extremum, and hitting time of the extremum via characteristic functions," Papers 2312.03929, arXiv.org.
    4. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient inverse $Z$-transform and pricing barrier and lookback options with discrete monitoring," Papers 2207.02858, arXiv.org, revised Jul 2022.
    5. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    6. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2025. "Lévy models amenable to efficient calculations," Stochastic Processes and their Applications, Elsevier, vol. 186(C).
    7. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.
    8. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    9. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2025. "Efficient evaluation of expectations of functions of a Lévy process and its extremum," Finance and Stochastics, Springer, vol. 29(2), pages 443-468, April.
    10. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    11. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    12. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2019. "Gauge transformations in the dual space, and pricing and estimation in the long run in affine jump-diffusion models," Papers 1912.06948, arXiv.org, revised Dec 2019.
    13. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2023. "Efficient inverse $Z$-transform: sufficient conditions," Papers 2305.10725, arXiv.org.
    14. Josef Danv{e}k & J. Posp'iv{s}il, 2020. "Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models," Papers 2006.13181, arXiv.org.
    15. Svetlana Boyarchenko & Sergei Levendorskiv{i}, 2024. "Correct implied volatility shapes and reliable pricing in the rough Heston model," Papers 2412.16067, arXiv.org.
    16. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Efficient evaluation of joint pdf of a L\'evy process, its extremum, and hitting time of the extremum," Papers 2312.05222, arXiv.org.
    17. Gero Junike & Hauke Stier, 2024. "Enhancing Fourier pricing with machine learning," Papers 2412.05070, arXiv.org.

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