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On the number of terms in the COS method for European option pricing

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  • Gero Junike

Abstract

The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number of terms N to approximate the truncated density by a cosine series. How to choose the truncation range is already known. Here, we are able to find an explicit and useful bound for N as well for pricing and for the sensitivities, i.e., the Greeks Delta and Gamma, provided the density of the log-returns is smooth. We further show that the COS method has an exponential order of convergence when the density is smooth and decays exponentially. However, when the density is smooth and has heavy tails, as in the Finite Moment Log Stable model, the COS method does not have exponential order of convergence. Numerical experiments confirm the theoretical results.

Suggested Citation

  • Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2303.16012
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    References listed on IDEAS

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    Cited by:

    1. Xiaoyu Shen & Fang Fang & Chengguang Liu, 2024. "The Fourier Cosine Method for Discrete Probability Distributions," Papers 2410.04487, arXiv.org, revised Oct 2024.
    2. Gero Junike & Hauke Stier, 2023. "From characteristic functions to multivariate distribution functions and European option prices by the damped COS method," Papers 2307.12843, arXiv.org, revised Jun 2024.
    3. Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Nov 2024.
    4. Gero Junike & Hauke Stier, 2024. "Enhancing Fourier pricing with machine learning," Papers 2412.05070, arXiv.org.

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