Recovering Linear Equations of XVA in Bilateral Contracts

Abstract

In this paper, we investigate conditions to convert nonlinear equations of XVA to linear equations. As we consider different borrowing/lending rates, pricing derivatives encounters a non-linear equation and this makes finding an analytic solution for the price with the XVA difficult. Thus, in general, we have to resort to expensive numerical computation. In most previous works, the attempts to find an analytic solution were conducted on a restrictive assumption that the borrowing/lending rates are same. We find conditions to relax the assumption. Moreover, the conditions are mild in the sense that it is often satisfied in practice.

Comment: 30 pages, 8 figures