Type \(G\) and spherical distributions on \(\mathbb R^d\)
It is well-known that the normality assumption for the return distribution is contravened in various important concrete situations (time series data, option prices, etc.). A solution to this status was the introduction and use of the type G family of processes as a suitable subclass of Lévy processes that allows retaining some of the Gaussian properties of the traditional Wiener process and yet to remain rich enough to incorporate processes with jumps and infinite variance. The purpose of this paper is to devise an exact convenient representation of type G distributions, provided that they are of spherical kind, and to investigate basic properties and examples of the proposed representation. The considered methodology of representing type G distributions reveals new mechanisms in extracting families of distributions that supply an insightful understanding of various applications in mathematical and computational finance. Three different examples are bestowed to illustrate and enrich the proposed method.
processes with jumps and infinite variance
variance mixtures of normal distributions
scientific article; zbMATH DE number 2167366