Improved Multilevel Monte Carlo Convergence using the Milstein Scheme

Mike Giles ()
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Mike Giles: Oxford University Computing Laboratory

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 343-358 from Springer

Abstract: Summary 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 differential equations. Numerical results for Asian, lookback, barrier and digital options demonstrate that the computational cost to achieve a root-mean-square error of ε is reduced to O(ε -2). This is achieved through a careful construction of the multilevel estimator which computes the difference in expected payoff when using different numbers of timesteps.

Keywords: European Option; Barrier Option; Asian Option; Multilevel Method; Brownian Path (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_20

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DOI: 10.1007/978-3-540-74496-2_20

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