Improved multilevel monte carlo convergence using the milstein scheme by Giles, M

“…In this paper we show that the Milstein scheme can be used to improve the convergence of the multilevel Monte Carlo method for scalar stochastic differential equations. Numerical results for Asian, lookback, barrier and digital options demonstrate that the computational cost to achieve a root-mean-square error of - is reduced to O(ε-2). …”

An adaptive random bit multilevel algorithm for SDEs by Giles, MB, Hefter, M, Mayer, L, Ritter, K

“…We study the approximation of expectations E(f (X)) for solutions X of stochastic differential equations and functionals f on the path space by means of Monte Carlo algorithms that only use random bits instead of random numbers. …”