New control variates for Lévy process models

We present a general control variate method for Monte Carlo estimation of the expectations of the functionals of Lévy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation between the increments of the original process and Brownian motion. In the suggested control variate framework, a similar functional of Brownian motion is used as a main control variate while some other characteristics of the paths are used as auxiliary control variates. The method is applicable for all types of Lévy processes for which the probability density function of the increments is available in closed form. We present the applications of our general approach for simulation of path dependent options. Numerical experiments confirm that our method achieves considerable variance reduction.