Multilevel Monte Carlo for exponential Lévy models

Michael B. Giles () and Yuan Xia ()
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Michael B. Giles: Oxford University
Yuan Xia: Oxford University

Finance and Stochastics, 2017, vol. 21, issue 4, No 4, 995-1026

Abstract: Abstract We apply the multilevel Monte Carlo method for option pricing problems using exponential Lévy models with a uniform timestep discretisation. For lookback and barrier options, we derive estimates of the convergence rate of the error introduced by the discrete monitoring of the running supremum of a broad class of Lévy processes. We then use these to obtain upper bounds on the multilevel Monte Carlo variance convergence rate for the variance gamma, NIG and α $\alpha$ -stable processes. We also provide an analysis of a trapezoidal approximation for Asian options. Our method is illustrated by numerical experiments.

Keywords: Multilevel Monte Carlo; Exponential Lévy models; Asian options; Lookback options; Barrier options; 65C05; 91G60 (search for similar items in EconPapers)
JEL-codes: C15 C63 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00780-017-0341-7

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