When Capital is a Funding Source: The XVA Anticipated BSDEs

Economic capital (EC) can be used as a funding source by banks, at a risk-free cost instead of the additional credit spread of the bank in the case of unsecured borrowing. This intertwining of EC and FVA leads to an... [ view full abstract ]

Economic capital (EC) can be used as a funding source by banks, at a risk-free cost instead of the additional credit spread of the bank in the case of unsecured borrowing. This intertwining of EC and FVA leads to an anticipated BSDE (ABSDE) for the FVA. Accounting further for the KVA (capital valuation adjustment) component of economic capital yields an (FVA, KVA) system of ABSDEs. We show that the (FVA, KVA) system of ABSDEs is well-posed, first for a bank without debt, and then in the realistic case of a defaultable bank, with all equations stopped before bank default.