Valuation Adjustments as Curvature: XVA in Financial Gauge Theory

Post-2008 derivative pricing requires adding a collection of valuation adjustments to the risk-free price: CVA (counterparty credit), DVA (own credit), FVA (funding), MVA (margin), KVA (capital), TVA (tax). The standard industry practice of computing each adjustment independently and summing the results is mathematically incorrect: it ignores the cross-terms between adjustments that arise from the joint dynamics of credit, funding, and capital costs.

This paper embeds XVA into Financial Gauge Theory (FGT). Each named adjustment is the curvature contribution of a distinct temporal fibre over the trade's tenor lattice. The total XVA is the holonomy of the joint connection on the tensor product of all six fibres. The cross-terms — wrong-way funding-credit, margin-funding overlap, DVA/FVA double-counting — are the off-diagonal mixed curvature components of this product bundle. They are missed by scalar addition because scalar addition is the zero-curvature approximation to the full holonomy.

The central theorem is that the Burgard–Kjaer semi-replication PDE is the flatness condition on the multi-fibre XVA bundle under the risk-neutral gauge — the exact generalisation of the HJM flatness theorem (Paper 296) to the six-fibre case.

The central proposition is the DVA/FVA non-redundancy criterion: DVA and FVA are linearly independent curvature contributions if and only if the bank's unsecured funding spread strictly exceeds its CDS-implied default intensity, $s_F(t) > \lambda_B(t)$. The excess $\ell = s_F - \lambda_B$ is the liquidity premium on the bank's own credit — an observable, market-testable quantity that resolves the Hull–White vs. Piterbarg DVA/FVA double-counting debate definitively.

KVA is qualitatively different from the other XVAs: it is a boundary constraint on the portfolio state space (the shadow price of regulatory capital), not a fibre curvature. The one context in which non-Abelian gauge structure may genuinely arise — multi-netting-set portfolio ordering non-commutativity — is identified and held as an open question.

This is Paper 299 in the FGT series. Companion papers: Paper 295 (Currency Bundles, doi:10.5281/zenodo.20242355), Paper 296 (Term Structure Bundles, doi:10.5281/zenodo.20244445), Paper 298 (Credit Bundles, doi:10.5281/zenodo.20257596), Paper 291 (Pacioli Manifold, doi:10.5281/zenodo.20229938).