Lending Values and Liquidity Risk

In this paper we show how to derive a liquidity adjusted lending value in the case where the collateral is given by a single stock. Following [12] and [7], the collateral market value is adjusted as a function of the position size based on the existence of a one-parameter exponential supply curve. The lending value is then determined as usual, i.e. such that the probability that after a margin call the collateral value falls below the client exposure is at most ϵ > 0. The curve parameter for a specific stock can be estimated from intraday data by means of a simple regression. Furthermore, we show that an affine model where the liquidity parameter characterizing the exponential supply curve is assumed to be a function of the Average Daily Trading Volume (ADTV) has an excellent predictive power. This implies that the ADTV can be used for a simple and direct computation of the liquidity parameter avoiding the use of the intraday data. Concrete examples highlight the impact of liquidity risk on the lending value.