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On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance

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  • Søren Asmussen

    (Aarhus University)

Abstract

We study the structure and properties of an infinite-activity CGMY Lévy process X $X$ with given skewness S $S$ and kurtosis K $K$ of X 1 $X_{1}$ , without a Brownian component, but allowing a drift component. The jump part of such a process is specified by the Lévy density which is C e − M x / x 1 + Y $C\mathrm {e}^{-Mx}/x^{1+Y}$ for x > 0 $x>0$ and C e − G | x | / | x | 1 + Y $C\mathrm {e}^{-G|x|}/|x|^{1+Y}$ for x

Suggested Citation

  • Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00482-x
    DOI: 10.1007/s00780-022-00482-x
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    1. 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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    More about this item

    Keywords

    Cumulant; Functional limit theorem; Log-return distribution; Exponentially tilted stable distribution; Moment method; Wasserstein distance;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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