The Impact of Funding Costs and Liquidity Risk on the Valuation of Derivatives and Banking Book Products

Abstract

Traditionally derivatives and other assets have been valued in isolation. The balance sheet of which a derivative position is part, was not included in the valuation. Recently, aspects of the valuation have been revised to incorporate certain elements of the balance sheet in the valuation. Examples are the debt valuation adjustment which incorporates default risk of the bank holding the derivative, and the funding valuation adjustment that some authors have proposed to include the cost of funding into the valuation. This paper investigates the valuation of derivatives and other assets as part of a balance sheet. In particular, funding costs, default risk and liquidity risk are considered. A valuation framework is developed under the elastic funding assumption. This assumption states that funding costs reflect the quality of the assets, and any change in asset composition is immediately reflected in the funding costs. The paper generalizes the result of Nauta 2012 that funding costs do not have an impact on the value of derivatives to cases including default risk. Furthermore a new model for the valuation of liquidity risk is developed. The result is that the liquidity spread, that is used for discounting cashflows of illiquid assets, can be expressed in terms of liquidation value of the asset, and the probability that the institution holding the asset needs to liquidate (part of its) assets. The resulting model is similar to existing models that include fixed funding costs, such as Burgard Kjaer 2011, with the difference that the funding spread is replaced by the liquidity spread. This has some important consequences, since the liquidity spread depends on the product and e.g. the size of the position, whereas the funding spread does not. Examples for banking book products and OTC call options are included to illustrate the framework.