We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a defaultable counterparty, but has incomplete information about her credit quality. By constraining the actual default intensity of the counterparty within an uncertainty interval , we derive both upper and lower bounds for the XVA process . We show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs introduce fundamental differences relative to classical credit risk valuation. The superhedging value 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.
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.
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