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 an accuracy of O(ε) is reduced from O(ε-3) to O(ε-2(logε)2). The analysis is supported, by numerical results showing significant computational savings. © 2008 INFORMS.
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