XVA Analysis From the Balance Sheet
Résumé
XVAs denote various counterparty risk related valuation adjustments that are applied to financial derivatives since the 2007-09 crisis. We root a cost-of-capital XVA strategy in a balance sheet perspective which is key in identifying the economic meaning of the XVA terms. Our approach is first detailed in a static setup that is solved explicitly. It is then plugged in the dynamic and trade incremental context of a real derivative banking portfolio. The corresponding cost-of-capital XVA strategy ensures to bank shareholders a submartingale equity process corresponding to a target hurdle rate on their capital at risk, consistently between and throughout deals. Set on a forward/backward SDE formulation, this strategy can be solved efficiently using GPU computing combined with deep learning regression methods in a whole bank balance sheet context. A numerical case study emphasizes the workability and added value of the ensuing pathwise XVA computations.
Mots clés
Counterparty risk balance sheet of a bank market incompleteness wealth transfer X-valuation adjustment (XVA) deep learning quantile regression Mathematics Subject Classification: 91B25 91B26 91B30 91G20 91G40 62G08 68Q32 JEL Classification: D52 G13 G24 G28 G33 M41
Counterparty risk
balance sheet of a bank
market incompleteness
wealth transfer
X-valuation adjustment (XVA)
deep learning
quantile regression
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