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In this paper, authors successfully construct a new algorithm for the newhigher order scheme of weak approximation of SDEs. The algorithm presented hereis based on [1][2]. Although this algorithm shares some features with thealgorithm presented by [3], algorithms themselves are completely different andthe diversity is not trivial. They apply this new algorithm to the problem ofpricing Asian options under the Heston stochastic volatility model and obtainencouraging results.  [1] Shigeo Kusuoka, "Approximation of Expectation of Diffusion Process andMathematical Finance," Advanced Studies in Pure Mathematics, Proceedings ofFinal Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp.147--165. [2] Terry Lyons and Nicolas Victoir, "Cubature on Wiener Space,"Proceedings of the Royal Society of London. Series A. Mathematical and PhysicalSciences 460 (2004), pp. 169--198. [3] Syoiti Ninomiya, Nicolas Victoir, "Weakapproximation of stochastic differential equations and application toderivative pricing," Applied Mathematical Finance, Volume 15, Issue 2 April2008, pages 107--121

A new weak approximation scheme of stochastic differential equations and the Runge-Kutta method