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In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC)simulation technique for Levy processes from Kuznetsov et al. [17] to pathfunctionals, in particular first passage times, overshoots, undershoots and thelast maximum before the passage time. Such functionals have many applications,for instance in finance (the pricing of exotic options in a Levy model) andinsurance (ruin time, debt at ruin and related quantities for a Levy insurancerisk process). The technique works for any Levy process whose running infimumand supremum evaluated at an independent exponential time allows sampling from.This includes classic examples such as stable processes, subclasses ofspectrally one sided Levy processes and large new families such as meromorphicLevy processes. Finally we present some examples. A particular aspect that isillustrated is that the WHMC simulation technique performs much better atapproximating first passage times than a `plain' Monte Carlo simulationtechnique based on sampling increments of the Levy process.

Applying the Wiener-Hopf Monte Carlo simulation technique for Levy  processes to path functionals such as first passage times, undershoots and  overshoots