# Lévy Measures

Lévy Measures

The structure of jumps of a Lévy process is determined by its Lévy (or characteristic) measure. For an -dimensional Lévy process, the Lévy measure of is given by the expected number, per unit time, of jumps whose size belongs to . This Demonstration compares the Lévy measures of some well-known stochastic processes that have been much used in mathematical finance. They have been divided into two groups: the jump diffusion group, consisting of the Merton and Kou models, and the pure jump processes group, consisting of the Variance Gamma and Normal Inverse Gaussian (NIG) models. The model parametrizations have been chosen to make the comparisons easier. Below the graphs of the densities of the Lévy measures, the total weights of the "small" and "large" jumps are displayed (see the Details section for further explanation). Place the mouse over the graph of a density function to see its name.

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