Abstract: Levy processes have been widely used to model financial assets since the 1990s. The reason of their widespread applications is mainly due to the fact that they provide more realistic models that capture discontinuous behaviors and stylized empirical statistical characteristics of time series data in economy and finance. However, when applied to derivative pricing, very few analytical results are available except for European options.  Therefore, one usually has to resort to numerical methods such as Monte Carlo simulation method.  The simulation method is so attractive  that it is very general and can also handle high dimensional problems very well.  In this short survey paper, we first provide an overview on Levy processes.  We then introduce Monte Carlo simulation method for Levy processes.  Finally, we discuss the two main simulation based gradient estimation methods: perturbation analysis and likelihood ratio method.

Key words:  Levy-driven model, Monte Carlo simulation, simulation optimization, gradient estimation