  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 defaultable bonds. The investor does
not know the return rate of her counterparty's bond, but 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 important 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. Our comparative statics analysis
indicates that credit contagion has a nonlinear effect on the replication
strategies and on the XVA.
