Abstract
The author presents a new discretization method of stochastic differential equations (SDEs) without proof. The method is a kind of K-scheme (Kusuoka approximation, Kusuoka-Lyons-Ninomiya-Victoir method). K-scheme is a new framework of the higher order discretization methods for approximating SDEs weakly, proposed by Kusuoka. Ninomiya-Victoir and Ninomiya-Ninomiya methods are known as practical realizations of K-scheme, and some extrapolations of these methods are proposed. The new method is higher order than these methods without the use of extrapolations, and the author applies it to a financial problem of derivative pricing.
