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 (log ϵ) 2 ). The analysis is supported by numerical results showing significant computational savings.

• EA
  Engineering and Physical Sciences Research Council

  Award: EP/E031455/1