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The variance gamma stochastic process is a three-parameter generalization of the Brownian motion process. It is an example of the finite variation Lévy process. It has infinitely many jumps in any time interval, but only finitely many jumps larger than any given size. Like all finite variation processes, it can be written as the difference of two increasing processes, in this case gamma processes.

The variance gamma process was introduced into option pricing by Madan and Seneta [1] and generalized by Madan, Carr, and Chang [2]. Explicit formulas for European style options can be given, generalizing the Black–Scholes formulas. The model has been shown to perform better than the Black–Scholes model under the "historical approach" [3].

[1] D. B. Madan and E. Seneta, "The Variance Gamma Process (V.G.) Model for Share Market Returns," Journal of Business 63(4) pp. 511-524.

[2] D. B. Madan, P. P. Carr, and E. C. Chang, "The Variance Gamma Process and Option Pricing," European Finance Review 2(1), 1998 pp. 79-105.

[3] K. Lam, E. Chang, and M. C. Lee, "An Empirical Test of the Variance Gamma Option Pricing Model," Pacific Basin Finance Journal 10(3), 2002 pp. 267-285.