A Closed-Form Solution to the Liquidity Discount Problem: With an Application to the Liquidity Crisis

Abstract

During the recent financial crisis, we witnessed unprecedented compressions of asset prices. In a recent paper, Chen [2012] proposed a liquidity discount model that can successfully explain large price falls. In this article, we provide alternative valuations to the Chen model. Building on the same framework, we provide a new polynomial representation of the liquidity discount. We also simplify the Chen model to a closed-form solution in a situation where there is no trading in the marketplace. We demonstrate in analytical forms that convexity in a security payoff is absolutely positively related to liquidity discounts.

Finally, we contribute to the literature in relating the Chen model to trading volume (e.g., Karpoff [1986, 1987]). Using the price and trading volume data of the nine largest financial firms in the United States, we find strong support of the Chen model.