General Multilevel Monte Carlo Methods for Pricing Discretely Monitored Asian Options

European Journal of Operational Research, 2020

Posted: 14 Jul 2020

Date Written: May 19, 2020

Abstract

We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at m fixed dates. For a variety of processes that can be simulated exactly, we prove that, for the same computational cost, our method yields an unbiased estimator with variance lower than the variance of the standard Monte Carlo estimator by a factor of order m. We show how to combine our approach with the Milstein scheme for processes driven by scalar stochastic differential equations, and with the Euler scheme for processes driven by multidimensional stochastic differential equations. Numerical experiments confirm that our method outperforms the conventional Monte Carlo algorithm by a factor proportional to m.

Keywords: Finance, Simulation, Asian option, Multilevel Monte Carlo method, Variance reduction

JEL Classification: C63,G13

Suggested Citation

Kahale, Nabil, General Multilevel Monte Carlo Methods for Pricing Discretely Monitored Asian Options (May 19, 2020). European Journal of Operational Research, 2020, Available at SSRN: https://ssrn.com/abstract=3631679

Nabil Kahale (Contact Author)

ESCP Business School ( email )

79, avenue de la République
Paris, 75011
France

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