Accounting for default risk in the valuation of financial derivatives has become increasingly important, especially since the 2007–8 financial crisis. Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear partial differential equation (PDE). We propose numerical methods for handling the nonlinearity in this PDE, the most efficient of which are the discrete penalty iteration methods. We first formulate a penalty iteration method for the case of European contingent claims and study its convergence. We then extend the method to the case of American contingent claims, which results in a double-penalty iteration. We also propose boundary conditions and their discretization for the XVA PDE problem in the case of a call option, a put option and a forward contract. Numerical results demonstrate the effectiveness of our methods.