Financial Market Liquidity and the Distribution of Prices

We establish a link between liquidity in a limit order book market and the existence of a unique stationary distribution of transactions prices. The main implication of the model, that illiquidity can lead to the lack of existence of a unique distribution, is investigated using a newly developed test for the ergodicity of a time series process. Using matched high-frequency trading data on identical financial instruments traded in a 24-hour market, we find that the hypothesis of the ergodicity of prices is rejected for the illiquid overnight market, implying that a unique stationary price distribution does not exist. The hypothesis cannot be rejected in a demonstrably liquid setting, suggesting that average price distributions and their evolution do not depend on initial conditions. Market design and variations in information environments over the course of the 24-hour day also are considered, but cannot explain the results