Multilevel path simulation for weak approximation schemes

2014/06/10 by Belomestny, Denis, Nagapetyan, Tigran
#65C05 #65C30 #Computational Finance (q-fin.CP) #FOS: Economics and business

paper · doi:10.48550/arxiv.1406.2581

Abstract

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for Lévy driven stochastic differential equations, and show that, given a weak convergence of order α≥ 1/2, the complexity of the corresponding "weak" MLMC estimate is of order ε^-2log ²(ε). The numerical performance of the new "weak" MLMC method is illustrated by several numerical examples.

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