Funding Cost and a New Capital Model

Hannah, Lincoln (2013): Funding Cost and a New Capital Model.

Abstract

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).

• Item Type: MPRA Paper
• Language: English
• Keywords: CVA - Credit Value Adjustment DVA - Debit Value Adjustment FVA - Funding Value Adjustment EL - Expected Loss Capital Debt CVA - Credit Value Adjustment DVA - Debit Value Adjustment FVA - Funding Value Adjustment PD – Probability of Default EL - Expected Loss Capital Debt Attribution
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

Christoph Burgard and Mats Kjaer, 2011, In the balance Risk Magazine - October 2011, SSRN - March 2011

John Hull and Alan White, 2012, The FVA debate Risk Magazine – August 2012 www.risk.net/risk-magazine/analysis/2188684/risk-25-the-fva-debate

John Hull and Alan White, 2013, Valuing Derivatives: Funding value Adjustments and Fair Value DefaultRisk.com – April 2013

Vladimir Piterbarg, 2010, Funding beyond Discounting: Collateral Agreements and Derivatives Pricing Risk Magazine - February 2010

Basel Committee on Banking Supervision – International Convergence of Capital Measurement an Capital Standards (Basel II) http://www.bis.org/publ/bcbs128.pdf

Dirk Tasche, 2007, Euler Allocation: Theory and Practice http://www.greta.it/credit/credit2007/thursday/1_Tasche.pdf