Title: Robust XVA,
Abstract: We introduce an arbitrage-free framework for robust valuation adjustments. An
investor trades a credit default swap portfolio with a risky counterparty, and
hedges credit risk by taking a position in the counterparty bond. The investor
does not know the expected rate of return of the counterparty bond, but he is
confident that it lies within an uncertainty interval. We derive both upper and
lower bounds for the XVA process of the portfolio, and show that these bounds
may be recovered as solutions of nonlinear ordinary differential equations. The
presence of collateralization and closeout payoffs leads to fundamental
differences with respect to classical credit risk valuation. The value of the
super-replicating portfolio cannot be directly obtained by plugging one of the
extremes of the uncertainty interval in the valuation equation, but rather
depends on the relation between the XVA replicating portfolio and the close-out
value throughout the life of the transaction.