The Variance-Gamma Distribution: A Review

Adrian Fischer, Robert Gaunt, Andrey Sarantsev

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
JournalStatistical Science
Publication statusAccepted/In press - 26 Feb 2024


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


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