Time changes for Levy processes

The goal of this paper is to consider pure jump Levy 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 Levy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Levy processes that are analytically tractable, in their characteristic functions and Levy densities, and hence are relevant for option pricing.