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 this method, we generate a process that is highly correlated with an underlying price process generated by the time-changed Lévy model. We then apply the characteristic function approach with a 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.