Before revision: In this paper, we investigate conditionsto convert nonlinear equations of XVA to linear equations. As we consider different borrowing/lendingrates, 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.
After revision: We discuss a binary nature of funding impacts. Under some conditions, funding is either cost or benefit, i.e., one of the lending / lending rates are same.