XVA of a Derivative on an Underlying Modelled by a Default Jump Process with an Analysis of CVA Wrong Way Risk for Bond Forwards

Abstract

We consider the valuation and risk management of derivatives on defaultable assets such as bonds taking into account funding (FVA), cash collateral, underlying default, counterparty default (CVA) and default correlation using joint default poisson process. The framework can be considered as an extension of the Black Scholes FVA/CVA framework of Bugard and Kjaer. The results are applied to bond forward contracts and total return swaps with early termination at underlying default.

Keywords: Black Scholes, defaultable underlying, bond derivatives, funding costs (FVA), counterparty credit value adjustment (CVA), underlying credit value adjustment, XVA, cash collateralization, bond forwards, total return swaps, wrong way Risk, default correlation

JEL Classification: G13