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March 2015 Applying the Wiener-Hopf Monte Carlo simulation technique for Lévy processes to path functionals
Albert Ferreiro-Castilla, Kees van Schaik
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J. Appl. Probab. 52(1): 129-148 (March 2015). DOI: 10.1239/jap/1429282611

Abstract

In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) 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 Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Lévy processes, and large new families such as meromorphic Lévy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a 'plain' Monte Carlo simulation technique based on sampling increments of the Lévy process.

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Albert Ferreiro-Castilla. Kees van Schaik. "Applying the Wiener-Hopf Monte Carlo simulation technique for Lévy processes to path functionals." J. Appl. Probab. 52 (1) 129 - 148, March 2015. https://doi.org/10.1239/jap/1429282611

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1319.65006
MathSciNet: MR3336851
Digital Object Identifier: 10.1239/jap/1429282611

Subjects:
Primary: 60G51 , 65C05 , 68U20

Keywords: exotic option pricing , First passage time , insurance risk process , Lévy process , Monte Carlo simulation , Multilevel Monte Carlo , overshoot , Wiener-Hopf decomposition

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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