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 exact return rate of her counterparty's bond, but she knows 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 closeout 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.

中文翻译：

---

健壮的XVA

我们引入了无套利框架来进行稳健的估值调整。投资者与有风险的交易对手交易信用违约掉期投资组合，并通过在可违约债券中持仓来对冲信用风险。投资者不知道对方债券的确切收益率，但她知道它处于不确定区间内。我们得出了投资组合的XVA过程的上限和下限，并表明这些界限可以作为非线性常微分方程的解而被恢复。抵押和清算收益的存在导致与经典信用风险评估有关的重大差异。不能通过在估值方程中插入不确定性区间的极值之一来直接获得超级复制投资组合的价值，而是取决于XVA复制资产组合和整个交易生命周期内的平仓价之间的关系。我们的比较静态分析表明，信用传染对复制策略和XVA具有非线性影响。