  In this paper, authors successfully construct a new algorithm for the new
higher order scheme of weak approximation of SDEs. The algorithm presented here
is based on [1][2]. Although this algorithm shares some features with the
algorithm presented by [3], algorithms themselves are completely different and
the diversity is not trivial. They apply this new algorithm to the problem of
pricing Asian options under the Heston stochastic volatility model and obtain
encouraging results.
  [1] Shigeo Kusuoka, "Approximation of Expectation of Diffusion Process and
Mathematical Finance," Advanced Studies in Pure Mathematics, Proceedings of
Final 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 Physical
Sciences 460 (2004), pp. 169--198. [3] Syoiti Ninomiya, Nicolas Victoir, "Weak
approximation of stochastic differential equations and application to
derivative pricing," Applied Mathematical Finance, Volume 15, Issue 2 April
2008, pages 107--121
