Realized Illiquidity

We study the theoretical and empirical properties of a simple measure of market illiquidity, namely the realized Amihud, which is defined as the ratio between the realized volatility and trading volume and which refines the popular price impact measure proposed by Amihud (2002). In our model, both price volatility and market liquidity are assumed to follow stochastic processes in continuous time. In this setting, characterized by stochastic volatility and liquidity, we prove that the realized Amihud provides a precise measurement of the inverse of integrated liquidity, that is, the integral of [...] over fixed-length periods (e.g., a day, a week, a month). We consider a number of alternative econometric specifications, hence highlighting the main dynamic and distributional properties of the realized Amihud, including jumps, clustering, and leverage effects.