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Multi-level Monte Carlo path simulation

Giles, M. B. (2006) Multi-level Monte Carlo path simulation. Technical Report. Unspecified. (Submitted)

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Abstract

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 an Euler discretisation, the computational cost to achieve an accuracy of $O(\epsilon)$ is reduced from $O(\epsilon^{-3})$ to $O(\epsilon^{-2} (\log \epsilon)^2)$. The analysis is supported by numerical results showing significant computational savings.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1120
Deposited By:Lotti Ekert
Deposited On:11 May 2011 10:30
Last Modified:11 May 2011 10:30

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