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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Bibliographic Details
Published in:Operations research Vol. 56; no. 3; pp. 607 - 617
Main Author: Giles, Michael B
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.05.2008
Institute for Operations Research and the Management Sciences
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0496