Department of Mathematics Calendar
Maxim Bichuch, Johns Hopkins University, Robust XVA
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We discuss the reasons for the introduction of Valuation Adjustments as a consequence of the financial crisis of 2007-9. We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a defaultable counterparty. 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. This is a joint work with Agostino Capponi and Stephan Sturm.