The Variance-Gamma Distribution: A Review

Adrian  Fischer; Robert Gaunt; Andrey  Sarantsev

doi:10.1214/24-STS929

The Variance-Gamma Distribution: A Review

Adrian Fischer
, Robert Gaunt
, Andrey Sarantsev

Probability

Research output: Contribution to journal › Article › peer-review

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Abstract

The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial
modelling and distributional approximation on Wiener space. In this review,
we provide an up-to-date account of the basic distributional theory of the
VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random
variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including
the aforementioned applications to financial modelling and distributional approximation on Wiener space.

Original language	English
Pages (from-to)	235-258
Journal	Statistical Science
Volume	40
Issue number	2
DOIs	https://doi.org/10.1214/24-STS929
Publication status	Published - 1 May 2025

Keywords

Variance-gamma distribution
distributional theory
estimation
variance-gamma process
financial modelling
approximation on Wiener space

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10.1214/24-STS929Licence: CC BY

Rates of Convergence in Multivariate Normal Approximation by Stein's Method
Gaunt, R. (PI)
1/03/24 → 28/02/27
Project: Research

Cite this

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title = "The Variance-Gamma Distribution: A Review",

abstract = "The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional approximation on Wiener space. In this review, we provide an up-to-date account of the basic distributional theory of the VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including the aforementioned applications to financial modelling and distributional approximation on Wiener space.",

keywords = "Variance-gamma distribution, distributional theory, estimation, variance-gamma process, financial modelling, approximation on Wiener space",

author = "Adrian Fischer and Robert Gaunt and Andrey Sarantsev",

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doi = "10.1214/24-STS929",

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journal = "Statistical Science",

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AU - Gaunt, Robert

AU - Sarantsev, Andrey

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N2 - The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional approximation on Wiener space. In this review, we provide an up-to-date account of the basic distributional theory of the VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including the aforementioned applications to financial modelling and distributional approximation on Wiener space.

AB - The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional approximation on Wiener space. In this review, we provide an up-to-date account of the basic distributional theory of the VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including the aforementioned applications to financial modelling and distributional approximation on Wiener space.

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KW - variance-gamma process

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KW - approximation on Wiener space

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EP - 258

JO - Statistical Science

JF - Statistical Science

IS - 2

ER -

The Variance-Gamma Distribution: A Review

Abstract

Keywords

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Rates of Convergence in Multivariate Normal Approximation by Stein's Method

Cite this