2013/06/17 by Albert Ferreiro-Castilla, Ferreiro-Castilla, Albert, Kees van Schaik +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1306.3923
openalex publication_date 2013/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC)\nsimulation technique for Levy processes from Kuznetsov et al. [17] to path\nfunctionals, in particular first passage times, overshoots, undershoots and the\nlast maximum before the passage time. Such functionals have many applications,\nfor instance in finance (the pricing of exotic options in a Levy model) and\ninsurance (ruin time, debt at ruin and related quantities for a Levy insurance\nrisk process). The technique works for any Levy process whose running infimum\nand supremum evaluated at an independent exponential time allows sampling from.\nThis includes classic examples such as stable processes, subclasses of\nspectrally one sided Levy processes and large new families such as meromorphic\nLevy processes. Finally we present some examples. A particular aspect that is\nillustrated is that the WHMC simulation technique performs much better at\napproximating first passage times than a `plain' Monte Carlo simulation\ntechnique based on sampling increments of the Levy process.\n