Consistent XVA Metrics Part II: Multi-Currency

Abstract

We present a consistent framework for computing shareholder and firm values of derivative portfolios in the presence of collateral, counterparty risk and funding costs in a multi-currency economy. The results extend the single currency economy results from Kjaer and the major difference is that the effective funding spreads now include cross currency basis spreads. This is a consequence of having to hedge the foreign exchange rate risks that arise from converting funding in one currency into collateral in another. The resulting valuation adjustments have been implemented in the forthcoming Bloomberg MARS XVA product.