This paper considers computational challenges to practically important problems related to pricing exotic interest rate derivatives, using the Kusuoka–Lyons–Ninomiya–Victoir scheme (KLNV-scheme) which is a higher-order discretization framework for performing weak approximations of stochastic differential equations. The author demonstrates the KLNV-scheme is even more effective for some types of practical high-dimensional problems, especially when close or approximate solutions to the involved ordinary differential equations can be found. Moreover, the numerical results show the proposed methods are 500 to more than 6000 times faster compared to the conventional methods.

本文使用 Kusuoka-Lyons-Ninomiya-Victoir 方案（KLNV-方案），这是一个用于执行随机微分方程弱近似的高阶离散化框架，考虑了与定价奇异利率衍生品相关的实际重要问题的计算挑战。作者证明了 KLNV 方案对于某些类型的实际高维问题更有效，尤其是当可以找到所涉及的常微分方程的接近或近似解时。此外，数值结果表明，与传统方法相比，所提出的方法快了 500 到 6000 倍以上。