Funding Cost and a New Capital Model

In asset and derivative pricing, funding costs and capital costs are usually considered separately. A derivative will be funded at a given rate such as OIS, LIBOR or the bank’s cost of borrowing, and a cost of capital will be added separately. This paper presents a model that combines the two, using funding attributions from a capital model based on the bank’s Expected Loss (EL) rather than the market standard Probability of Default (PD). The basic idea is: A bank could fund a new asset with the combination of debt and equity that leaves its EL constant. The debt-equity mix gives a funding cost that reflects the risk of the asset rather than the bank, so is a more appropriate rate for assessing the asset than the bank’s Weighted Average Cost of Capital (WACC). In this way, the model facilitates decisions consistent with the Modigliani and Miller theorem (i.e. decisions based on the risk of the asset rather than the bank’s cost of funding). A result of the model is that, in accordance with the view of Hull and White (2012), the cost of funding a derivative is given by its CVA-DVA adjusted price and does not require an additional Funding Value Adjustment (FVA). Some of the funding ideas produced by the model have already been suggested by others, such as Piterbarg (2010) and Burgard and Kjaer (2011).