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Time Changes for Lévy Processes
Authors:Hélyette Geman  Dilip B Madan  & Marc Yor
Institution:UniversitéParis IX Dauphine and ESSEC,;University of Maryland,;UniversitéParis VI–Laboratoire de Probabilités
Abstract:The goal of this paper is to consider pure jump Lévy processes of finite variation with an infinite arrival rate of jumps as models for the logarithm of asset prices. These processes may be written as time-changed Brownian motion. We exhibit the explicit time change for each of a wide class of Lévy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Lévy processes that are analytically tractable, in their characteristic functions and Lévy densities, and hence are relevant for option pricing.
Keywords:purely discontinuous processes  finite variation processes  Brownian excursions  infinite activity  completely monotone Lévy density
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