Positive XVAs

Stéphane Crépey ()
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Stéphane Crépey: UFR Mathématiques UPCité - UFR Mathématiques [Sciences] - Université Paris Cité - UPCité - Université Paris Cité, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

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Abstract: 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 h on their capital at risk. The resulting all-inclusive XVA formula reads (CVA + FVA + KVA), 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.

Keywords: Counterparty risk market incompleteness credit valuation adjustment (CVA) funding valuation adjustment (FVA) capital valuation adjustment (KVA) wealth transfer. central counterparties (CCP) Mathematics Subject Classification: 91B25 91B26 91B30 91G20 91G40 JEL Classification: D52 G13 G24 G28 G33 M41; Counterparty risk; market incompleteness; credit valuation adjustment (CVA); funding valuation adjustment (FVA); capital valuation adjustment (KVA); wealth transfer. central counterparties (CCP) (search for similar items in EconPapers)
Date: 2022
New Economics Papers: this item is included in nep-rmg
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Published in Frontiers of Mathematical Finance, 2022

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