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

Albert Ferreiro-Castilla and Kees van Schaik

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

Date: 2013-06, Revised 2014-03
New Economics Papers: this item is included in nep-cmp, nep-ets and nep-ore
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