  We study the semilinear partial differential equation (PDE) associated with
the non-linear BSDE characterizing buyer's and seller's XVA in a framework that
allows for asymmetries in funding, repo and collateral rates, as well as for
early contract termination due to counterparty credit risk. We show the
existence of a unique classical solution to the PDE by first proving the
existence and uniqueness of a viscosity solution and then its regularity. We
use the uniqueness result to conduct a thorough numerical study illustrating
how funding costs, repo rates, and counterparty credit risk contribute to
determine the total valuation adjustment.
