Credit, funding, margin, and capital valuation adjustments for bilateral portfolios

Abstract

We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crépey (2017), whereby so-called contra-liabilities and cost of capital are charged by the bank to its clients, on top of the fair valuation of counterparty risk, in order to account for the incomplete-ness of this risk. The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA, consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread. Our funding cost for variation margin (FVA) is defined asymmetrically since there is no benefit in holding excess capital in the future. Capital is fungible as a source of funding for variation margin, causing a material FVA reduction. We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin (MVA). Our capital valuation adjustment (KVA) is defined as a risk premium, i.e. the cost of remunerating shareholder capital at risk at some hurdle rate.