Multilevel Monte Carlo Path Simulation

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve...

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Vydáno v:	Operations research Ročník 56; číslo 3; s. 607 - 617
Hlavní autor:	Giles, Michael B
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Linthicum, MD INFORMS 01.05.2008 Institute for Operations Research and the Management Sciences
Témata:	Algorithms Analysis analysis of algorithms Applied sciences Approximation Brownian motion Complexity theory Computational complexity Cost estimates efficiency Estimation bias Estimators Eulers equations Exact sciences and technology finance Heuristic Heuristics Mathematical extrapolation Monte Carlo method Monte Carlo methods Monte Carlo simulation Operational research and scientific management Operational research. Management science Perceptron convergence procedure Portfolio theory simulation Simulation methods Stochastic models Studies United States Euler equation Monte Carlo method Lipschitz condition Differential equation Finance Computational complexity Modeling Multigrid analysis of algorithms: computational complexity Algorithm complexity simulation: efficiency Lipschitz function Algorithm analysis Stochastic equation
ISSN:	0030-364X, 1526-5463
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Shrnutí:	We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O ( ) is reduced from O ( –3 ) to O ( –2 (log ) 2 ). The analysis is supported by numerical results showing significant computational savings.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0030-364X 1526-5463
DOI:	10.1287/opre.1070.0496