Three-Toed Sloth

Limit Orders and Indirect Inference

My first Ph.D. student, Linqiao Zhao, jointly supervised with Mark Schervish, has just successfully defended her dissertation:

"A Model of Limit-Order Book Dynamics and a Consistent Estimation Procedure" [PDF, 2.8 M]

Abstract: A limit order is an order to buy or sell a certain number of shares of a financial instrument at a specified price or better. A market's limit order book collects all its outstanding limit orders, and changes through the arrival of orders, including matching new orders against old ones. Despite being extensively used in contemporary exchanges, the dynamics of limit-order books are still not understood well. In this thesis, we propose a minimal model for the dynamics of whole limit order books, based on a self-exciting stochastic process of order flows. However, the data available are not time series of entire books, but rather of small parts of the book, so that almost all of the data is missing, and very much not "missing at random". To fit our model to the actual data with its complicated, history-dependent censoring, we use a relatively new technique for simulation-based estimation, indirect inference. We extend this methodology, proving new theorems on the consistency and asymptotic normality of indirect inference under weaker conditions than those previously established.

The fitted model captures important features of observable data from limit-order books, and exhibits important advantages over existing benchmark models. We point out some of the remaining discrepancies between our model and the data, and discuss how the model could be modified to accommodate them.

This is the culmination of years of hard work and determination on Linqiao's part. I'm very proud to have helped. Congratulations, Dr. Zhao!

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