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Precise option pricing by the COS method--How to choose the truncation range

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  • Gero Junike
  • Konstantin Pankrashkin

Abstract

The Fourier cosine expansion (COS) method is used for pricing European options numerically very fast. To apply the COS method, a truncation range for the density of the log-returns need to be provided. Using Markov's inequality, we derive a new formula to obtain the truncation range and prove that the range is large enough to ensure convergence of the COS method within a predefined error tolerance. We also show by several examples that the classical approach to determine the truncation range by cumulants may lead to serious mispricing. Usually, the computational time of the COS method is of similar magnitude in both cases.

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  • 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.
    • Handle: RePEc:arx:papers:2109.01030
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    Cited by:

    1. A. Aimi & C. Guardasoni & L. Ortiz-Gracia & S. Sanfelici, 2023. "Fast Barrier Option Pricing by the COS BEM Method in Heston Model," Papers 2301.00648, arXiv.org, revised Jan 2023.
    2. Carole Bernard & Gero Junike & Thibaut Lux & Steven Vanduffel, 2024. "Cost-efficient payoffs under model ambiguity," Finance and Stochastics, Springer, vol. 28(4), pages 965-997, October.
    3. Xiaoyu Shen & Fang Fang & Chengguang Liu, 2024. "The Fourier Cosine Method for Discrete Probability Distributions," Papers 2410.04487, arXiv.org, revised Oct 2024.
    4. Zhang, Zhimin & Zhong, Wei, 2024. "Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    5. Brignone, Riccardo & Gonzato, Luca, 2024. "Exact simulation of the Hull and White stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    6. 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.
    7. Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.
    8. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    9. Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Nov 2024.
    10. Gijs Mast & Xiaoyu Shen & Fang Fang, 2023. "Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion," Papers 2311.12575, arXiv.org.

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