Positive XVAs

Abstract

<p style='text-indent:20px;'>Since the 2008 crisis, derivative dealers charge to their clients various add-ons, dubbed XVAs, meant to account for counterparty risk and its capital and funding implications. As banks cannot replicate jump-to-default related cash flows, deals trigger wealth transfers and shareholders need to set capital at risk. We devise an XVA policy, whereby so called contra-liabilities and cost of capital are sourced from bank clients at trade inceptions, on top of the fair valuation of counterparty risk, in order to guarantee to the shareholders a hurdle rate <inline-formula><tex-math id="M1">\begin{document}$ h $\end{document}</tex-math></inline-formula> on their capital at risk. The resulting all-inclusive XVA formula reads (<inline-formula><tex-math id="M2">\begin{document}$ {{{\rm{CVA}}} }+{{{\rm{FVA}}}}+{{{\rm{KVA}}}} $\end{document}</tex-math></inline-formula>), where C sits for credit, F for funding, and where the KVA is a cost of capital risk premium. All these XVA metrics are portfolio-wide, nonnegative and, despite the fact that we include the default of the bank itself in our modeling, they are ultimately unilateral. This makes them naturally in line with the requirement that capital at risk and reserve capital should not decrease simply because the credit risk of the bank has worsened. An application of this approach to a dealer bank reveals, in particular, the XVA implications of the centrally cleared hedging side of the derivative portfolio of the bank.</p>