基于klnv格式的前向后SDEs高阶离散化方法及其在XVA定价中的应用

Q3 Mathematics

Applied Mathematical Finance Pub Date : 2019-05-04 DOI:10.1080/1350486X.2019.1637268

S. Ninomiya, Yuji Shinozaki

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引用次数: 4

摘要

摘要本文提出了一种新的高阶正反向随机微分方程离散化方法。在该方法中，前向分量采用离散随机变量的Kusuoka-Lyons-Ninomiya-Victoir格式进行离散化，后向分量采用与前向分量离散化方法一致的高阶数值积分方法，采用基于树的分支算法。本文提出的方法适用于XVA定价，特别是信用估值调整。数值结果表明，该方法能达到预期的理论阶数和计算效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing

ABSTRACT 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.

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来源期刊

Applied Mathematical Finance Economics, Econometrics and Finance-Finance

CiteScore

2.30

自引率

0.00%

发文量

期刊介绍： The journal encourages the confident use of applied mathematics and mathematical modelling in finance. The journal publishes papers on the following: •modelling of financial and economic primitives (interest rates, asset prices etc); •modelling market behaviour; •modelling market imperfections; •pricing of financial derivative securities; •hedging strategies; •numerical methods; •financial engineering.