We present a general control variate method for simulating path dependent options under Lévy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option...

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Lévy processes that is based on the Wiener–Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology....