Evaluating Liquidity Measures

Abstract

We propose to numerical solve for the equilibrium in a dynamic limit order market with a market maker and a large trader. Using the simulated data, we will evaluate commonly used measures of transaction costs and liquidity, such as the Amihud illiquidity measure, Kyle's, the PIN measure and spread measures. Varying the structural parameters of the model, such as the gains to trade, the degree of asymmetric information, the arrival rate of traders and the volatility of the underlying cash flows we can determine how each of these measures changes with changes in the economic fundamentals. As all these measures have been used to explain asset returns, this exercise will allow us to determine which economic fundamentals are priced. We propose to solve a model with risk-neutral agents who arrive randomly at the market for an asset that has both common and private components to its value. Agents will have different information about the common value, i.e., the present value of the future cash flows on the asset. Thus, there will be adverse selection: prior to his first entry in to the market, each agent chooses whether to buy information about the fundamental value of the asset. An informed agent views the current expected value of the cash flows on each entry, where as an uninformed agent forms an estimate of this value based on market observables. On arrival, each agent chooses either to buy or sell one share. If his order does not execute, here visits the market and can revise his order. Thus, agents face a dynamic problem: the actions they take at any point in time incorporate the possibility of future reentry. We will incorporate a market maker into this framework. Specifically, there will be an uninformed agent who is always in the market who bears a cost of holding inventories. In addition, we will introduce a large trader who submits market orders within a short time period. The out put of the model will be a time series of limit order books, including cancellations and transactions. In addition, we will observe market maker participation rates and inventories, and how the large trader splits his orders. Using this time series, we will construct standard transaction cost proxies. We will then vary the underlying parameters in the model to measure the changes in these proxies.