Multi-level 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 an Euler discretisation, the computational cost to achiev...
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| Format: | Report |
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Unspecified
2006
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| Streszczenie: | 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. |
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