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Improved multilevel Monte Carlo convergence using the Milstein scheme.

Abstract:
In this paper we show that the Milstein scheme can be used to improve the convergence of the multilevel Monte Carlo method for scalar stochastic diferential equations. Numerical results for Asian, lookback, barrier and digital options demonstrate that the computational cost to achieve a root-mean-square error of Ο is reduced to Ο(ε-2). This is achieved through a careful construction of the multilevel estimator which computes the diference in expected payoff when using diferent numbers of timesteps.

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Publisher:
Oxford-Man Institute of Quantitative Finance
Series:
Working Papers
Publication date:
2007-01-01
Language:
English
UUID:
uuid:1b463f64-8809-4488-8027-4faf376e91e9
Local pid:
oai:economics.ouls.ox.ac.uk:13019
Deposit date:
2011-08-16

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