Rough Paths based Numerical Algorithms in Computational Finance. - Gyurkó, L; Lyons, T (Oxford-Man Institute of Quantitative Finance, 2008)
The paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probably earlier, is based on locally deriving and solving random ordinary differential equations. A sufficient condition on the accuracy of the numerical ODE solver is given to ensure the global order is g1/2 if the local order is g. We also point out some practical solutions which make the high order schemes tractable.