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Traditionally derivatives have been valued in isolation. The balance sheet of which a derivative position is part, was not included in the valuation. Recently however, aspects of the valuation have been revised to incorporate certain elements of the balance sheet. 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 as part of a balance sheet. In particular, the paper considers funding costs, default risk and liquidity risk. 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 result is that funding costs should not affect the value of derivatives. Furthermore, a new model for pricing liquidity risk is described. The paper highlights that the liquidity spread, used for discounting cashflows of illiquid assets, should be expressed in terms of the liquidation value (LV) of the asset, and the probability that the institution holding the asset needs to liquidate its assets.

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This paper describes a model for the valuation of assets on a bank balance sheet with liquidity risk. The new feature of this model is that it explicitly incorporates the funding term of an asset. The inclusion of the funding term is important since it determines the expected liquidation loss. By minimizing the sum of the expected liquidation loss and funding costs the optimal funding term and value of the asset can be determined. This paper applies the model to single cash flows, loans, bonds, and derivatives. Also, the calibration to LIBOR basis spreads is discussed.

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