Xinyun Chen is currently an Assistant Professor in Finance at Wuhan University. She received her Ph.D in Operations Research from Columbia University in 2014. Her research interests include applied probability, Monte Carlo method and their applications in financial markets. She has published papers in journals including Annals of Applied Probability, Mathematics of Operations Research and Accounting and Finance. Before joining Wuhan University, she was an Assistant Professor in the Department of Applied Mathematics and Statistics at Stony Brook University and received research funding from NSF.
How much of the structure of a Limit Order Book (LOB) can be recovered by only observing the trade and quote (TAQ) sequence? In this paper we study the queueing dynamics in the LOB which, surprisingly, allows us to recover the LOB of stocks having relatively large spread with reasonable empirical accuracy. In particular, we are able to estimate the time-average order depth on almost all price levels of interest in the LOB by observing only the bid/ask price at the times of trades. As applications, we can use the result to estimate the price impact of trades and size of hidden orders. Our approach starts from a Markovian queueing model for the LOB dynamics. We apply a multi-scale analysis on the model to obtain a closed-form expression connecting the trade price change distribution and the LOB structure, which enables the recovery of LOB from the TAQ sequence. Our approach is also applicable to extended models with autocorrelated and state-dependent order ows in the LOB.
Key words: Limit order book, Market liquidity, Multi-scale model