Structured XVAs : Diffusive Portfolios

In this paper, a continuous-time, structural model of a dealer-bank is presented to derive fair value equations for credit-risky financial products that are not perfectly hedged. The impact these contracts have on the dealer-bank's earnings volatility, and consequently, their solvency and financing costs, is taken into account. Explicit relationships between credit, debit, funding, and capital valuation adjustments (CVA, DVA, FVA, and KVA, respectively) are established, highlighting the interdependencies between unhedged credit risk and financing adjustments. To illustrate the practical application of the model, several straightforward numerical examples are provided