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In Kuznetsov et al. (2011) a new Monte Carlo simulation technique wasintroduced for a large family of Levy processes that is based on theWiener-Hopf decomposition. We pursue this idea further by combining theirtechnique with the recently introduced multilevel Monte Carlo methodology.Moreover, we provide here for the first time a theoretical analysis of the newMonte Carlo simulation technique in Kuznetsov et al. (2011) and of itsmultilevel variant for computing expectations of functions depending on thehistorical trajectory of a Levy process. We derive rates of convergence forboth methods and show that they are uniform with respect to the "jump activity"(e.g. characterised by the Blumenthal-Getoor index). We also present a modifiedversion of the algorithm in Kuznetsov et al. (2011) which combined with themultilevel methodology obtains the optimal rate of convergence for general Levyprocesses and Lipschitz functionals. This final result is only a theoreticalone at present, since it requires independent sampling from a triple ofdistributions which is currently only possible for a limited number ofprocesses.

Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisation