The Semi-Hyperbolic Distribution and Its Applications

Roman V. Ivanov ()
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Roman V. Ivanov: Laboratory of Control under Incomplete Information, V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russia

Stats, 2023, vol. 6, issue 4, 1-21

Abstract: This paper studies a subclass of the class of generalized hyperbolic distribution called the semi-hyperbolic distribution. We obtain analytical expressions for the cumulative distribution function and, specifically, their first and second lower partial moments. Using the received formulas, we compute the value at risk, the expected shortfall, and the semivariance in the semi-hyperbolic model of the financial market. The formulas depend on the values of generalized hypergeometric functions and modified Bessel functions of the second kind. The research illustrates the possibility of analysis of generalized hyperbolic models using the same methodology as is employed for the well-established variance-gamma model.

Keywords: generalized hyperbolic distribution; semi-hyperbolic distribution; hypergeometric function; Bessel function; value-at-risk; expected shortfall; semivariance (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:6:y:2023:i:4:p:71-1146:d:1264669

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