A general control variate method for time-changed Lévy processes: An application to options pricing
We propose a new control variate method combined with a characteristic function approach for pricing path-dependent options under time-changed Lévy models. In our method, we generate a highly-correlated process with an underlying price process generated by the time-changed Lévy model. We then apply the characteristic function approach with the fast Fourier transform to obtain the expected payoff of the corresponding option under the correlated process. In numerical experiments, we employ three types of path-dependent options and six types of time-changed Lévy models to confirm the efficiency of our method. To the best of our knowledge, this paper is the first to develop an efficient control variate method for time-changed Lévy models.