Multilevel Monte Carlo Methods
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
WSC '04 Proceedings of the 36th conference on Winter simulation
Fast Pricing of Basket Default Swaps
Operations Research
Multilevel Monte Carlo Path Simulation
Operations Research
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The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.