On irregular functionals of SDEs and the Euler scheme

Abstract

We prove a sharp upper bound for the error in terms of moments of X - ̂X, where X and ̂X are random variables and the function g is a function of bounded variation. We apply the results to the approximation of a solution to a stochastic differential equation at time T by the Euler scheme, and show that the approximation of the payoff of the binary option has asymptotically sharp strong convergence rate 1/2. This has consequences for multilevel Monte Carlo methods. © Springer-Verlag 2009.