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.