Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing
Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing
复制标题
使用 KLNV 方案的前向-后向 SDE 高阶离散化方法及其在 XVA 定价中的应用
DOI：
10.1080/1350486x.2019.1637268
复制
发表时间：
2019
影响因子：
--
通讯作者：
Shinozaki Yuji
中科院分区：
文献类型：
--
作者：
Ninomiya Syoiti;Shinozaki Yuji
提出了一种新的正倒向随机微分方程高阶离散方法。在所提出的方法中，前向分量离散使用Kusuoka-Lyons-Ninomiya-Victoir计划与离散随机变量和向后分量使用高阶数值积分方法一致的离散方法的前向分量，通过使用基于树的分支算法。本文提出的方法适用于XVA定价，特别是信用评估调整。数值结果表明，该方法可以达到预期的理论阶数和计算效率。
This study proposes new higher-order discretization methods of forward-backward stochastic differential equations. In the proposed methods, the forward component is discretized using the Kusuoka–Lyons–Ninomiya–Victoir scheme with discrete random variables and the backward component using a higher-order numerical integration method consistent with the discretization method of the forward component, by use of the tree based branching algorithm. The proposed methods are applied to the XVA pricing, in particular to the credit valuation adjustment. The numerical results show that the expected theoretical order and computational efficiency could be achieved.