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Precise quantile function estimation from the characteristic function

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  • Junike, Gero

Abstract

We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the quantile function is typically several orders of magnitude larger than the numerical error of the cumulative distribution function for probabilities close to zero or one. We introduce the COS method for computing the quantile function. This method converges exponentially when the density is smooth and has semi-heavy tails and all parameters necessary to tune the COS method are given explicitly. Finally, we numerically test our theoretical results on the normal-inverse Gaussian and the tempered stable distributions.

Suggested Citation

  • Junike, Gero, 2025. "Precise quantile function estimation from the characteristic function," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000409
    DOI: 10.1016/j.spl.2025.110395
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    References listed on IDEAS

    as
    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. Chunfa Wang, 2017. "Pricing European Options by Stable Fourier-Cosine Series Expansions," Papers 1701.00886, arXiv.org, revised Jan 2017.
    4. William T. Shaw & Jonathan McCabe, 2009. "Monte Carlo sampling given a Characteristic Function: Quantile Mechanics in Momentum Space," Papers 0903.1592, arXiv.org.
    5. Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.
    Full references (including those not matched with items on IDEAS)

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