Applications of the Replication Method for XVAs

Abstract

Following in using zero-cost trade-able hedge instruments, we show that many forms of the valuation equations for PV and XVAs presented in the literature can be seen as particular cases of a more generic Replication framework. The convenient split between the effects of hedging our own default risk and funding obtained from the assumption of hedging with repo-able bonds allows for a systematic classification of the valuation equations according to their funding strategies. We describe strategies justifying for instance asymmetric funding in linear valuation by using three funding bonds. The Funding Invariance principle (Elouerkhaoui, 2016) i.e. the invariance against the choice of risk-free rate, is seen as a natural consequence of the Replication applied to the total risky derivative and is valid for all valuations derived from it. GVA, the adjustment when PV is discounted differently from the close-out amount, is crucial for the Funding Invariance to hold and allows a company to choose its PV discount rate with flexibility. Other applications of the Replication method include avoidance of double-counting and emergence of DVA2 and its counterpart CVA2.

Keywords: XVAs, Replication, FVA, DVA2, Funding Invariance

JEL Classification: G10