Measuring Liquidity with Return Volatility: an Analytical Approach Based on Heavy-Tailed Censored-GARCH Model

The measurement of liquidity based on low-frequency data is a crucial issue in the financial market microstructure literature. This paper extends the commonly used LOT liquidity model by incorporating the characterization of the volatility dynamics and distributional properties of return series, thereby significantly improving both the goodness-of-fit of liquidity model and the estimation performance of the existing low-frequency liquidity measures. The new models, which have a special form of heavy-tailed Censored-GARCH model, have challenges in estimation. We then provide an approximate maximum likelihood estimation method to circumvent this problem. A real data analysis is conducted to evaluate the performance of the new liquidity measures. The results show overwhelming evidence that our new measures have advantages over the existing measures in both estimation error and correlation coefficient with high-frequency bid-ask spread. The robustness check analysis further illustrates that the advantages of our new measures are stable across different stock industries and different turnover levels.