Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes

Abstract

Constructing \Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the \emph{a-reminder} of their self-decomposable stationary laws. In the present study we fully characterize the Lévy triplet of these a-reminder s and we provide a general framework to deduce the transition laws of the finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein-Uhlenbeck processes related to such distributions, with the further advantage of adopting a procedure computationally more efficient than those already available in the existing literature.

28 pages, 3 Figure, 4 Tables

References in corpus (4)

• Tempered stable distributions and processes
• Fast Pricing of Energy Derivatives with Mean-reverting Jump-diffusion Processes
• Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives
• An Exact Method For Simulating Rapidly Decreasing Tempered Stable Distributions