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Failure of Fourier pricing techniques to approximate the Greeks

Author

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  • Tobias Behrens
  • Gero Junike
  • Wim Schoutens

Abstract

The Greeks Delta and Gamma of plain vanilla options play a fundamental role in finance, e.g., in hedging or risk management. These Greeks are approximated in many models such as the widely used Variance Gamma model by Fourier techniques such as the Carr-Madan formula, the COS method or the Lewis formula. However, for some realistic market parameters, we show empirically that these three Fourier methods completely fail to approximate the Greeks. As an application we show that the Delta-Gamma VaR is severely underestimated in realistic market environments. As a solution, we propose to use finite differences instead to obtain the Greeks.

Suggested Citation

  • Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2306.08421
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    References listed on IDEAS

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    6. Junike, Gero & Pankrashkin, Konstantin, 2022. "Precise option pricing by the COS method—How to choose the truncation range," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    7. Gero Junike & Konstantin Pankrashkin, 2021. "Precise option pricing by the COS method--How to choose the truncation range," Papers 2109.01030, arXiv.org, revised Jan 2022.
    8. 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.
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