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Greeks' pitfalls for the COS method in the Laplace model

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  • Tobias Behrens
  • Gero Junike

Abstract

The Greeks Delta, Gamma and Speed are the first, second and third derivatives of a European option with respect to the current price of the underlying asset. The Fourier cosine series expansion method (COS method) is a numerical method for approximating the price and the Greeks of European options. We develop a closed-form expression of Speed for various European options in the Laplace model and we provide sufficient conditions for the COS method to approximate Speed. We show empirically that the COS method may produce numerically nonsensical results if theses sufficient conditions are not met.

Suggested Citation

  • Tobias Behrens & Gero Junike, 2023. "Greeks' pitfalls for the COS method in the Laplace model," Papers 2306.08421, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2306.08421
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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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    11. Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.
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