Adding Stochastic Credit and Funding to XVA Calculations

Abstract

It is widely accepted that the correlations among credit spreads, funding spreads, and market risk factors, e.g. interest rates, can have a material impact on XVAs. In this paper we study how this impact can be estimated without running a full-blown XVA model, in which counterparty default probabilities and funding spreads are simulated alongside the market risk factors that determine the future exposures. This problem can arise in different contexts, e.g. pricing, model validation, reserve calculations, or prudent valuation adjustments, if the primary XVA framework used for valuations does not account for these correlations. We show that these effects can be estimated very accurately using the XVA values and sensitivities produced by an XVA model with deterministic (or rather, independent) credit and funding spreads, and combining them with certain product-independent covariance terms computed using a separate model, capable of simulating default intensities and funding spreads together with the relevant market risk factors.