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A Note on the Conditions for COS Convergence

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  • Qinling Wang
  • Xiaoyu Shen
  • Fang Fang

Abstract

We study the truncation error of the COS method and give simple, verifiable conditions that guarantee convergence. In one dimension, COS is admissible when the density belongs to both L1 and L2 and has a finite weighted L2 moment of order strictly greater than one. We extend the result to multiple dimensions by requiring the moment order to exceed the dimension. These conditions enlarge the class of densities covered by previous analyses and include heavy-tailed distributions such as Student t with small degrees of freedom.

Suggested Citation

  • Qinling Wang & Xiaoyu Shen & Fang Fang, 2025. "A Note on the Conditions for COS Convergence," Papers 2512.02745, arXiv.org.
    • Handle: RePEc:arx:papers:2512.02745
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
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