XVA Analysis From the Balance Sheet

Claudio Albanese, Stéphane Crépey (), Rodney Hoskinson and Bouazza Saadeddine ()
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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: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2021
Note: View the original document on HAL open archive server: https://hal.science/hal-03910125v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published in Quantitative Finance, 2021, 21 (1), pp.99-123. ⟨10.1080/14697688.2020.1817533⟩

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Working Paper: XVA Analysis From the Balance Sheet (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03910125

DOI: 10.1080/14697688.2020.1817533

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