Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Levy process. Working with Levy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Levy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same...