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

Søren Asmussen ()
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Søren Asmussen: Aarhus University

Finance and Stochastics, 2022, vol. 26, issue 3, No 1, 383-416

Abstract: 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

Keywords: Cumulant; Functional limit theorem; Log-return distribution; Exponentially tilted stable distribution; Moment method; Wasserstein distance; 91–10; 60E07; 60K50 (search for similar items in EconPapers)
JEL-codes: C02 C46 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-022-00482-x

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