Strategic Foundation for the Tail Expectation in
Limit Order Book Markets
A Talk by Dr. Lawrence R. Glosten
We analyze the strategic interactions of liquidity suppliers quoting on a limit order book. In an environment with noise traders and informed traders trading on news we show that there is an equilibrium that feature quoters using mixed strategies; each offering the same quantity of shares at random prices (and, of course, random bid prices). These random prices with the associated quantities form the market quotes and the depth of book, or price schedule. There are equilibria with a smaller number of quoters quoting a larger number of shares and equilibria with a larger number of quoters quoting a smaller number of shares. Considering a sequence of equilibria with the number of quoters getting large, we establish that the stochastic equilibrium price schedule converges to the zero profit deterministic competitive price schedule. An offer (or bid) is characterized as the expectation of the future value conditional on the offer being picked off by a larger buy (or sell) order.
(Joint work with Shmuel Baruch, University of Utah)
Lawrence R. Glosten is the S. Sloan Colt Professor of Banking and International Finance at Columbia Business School. He is also co-director (with Merritt Fox and Ed Greene) of the Program in the Law and Economics of Capital Markets at Columbia Law School and Columbia Business School and is an adjunct faculty member at the Law School. He has been at Columbia since 1989, before which he taught at the Kellogg Graduate School of Management at Northwestern University, and has held visiting appointments at the University of Chicago and the University of Minnesota. He has published articles on the microstructure and industrial organization of securities markets; the relationship between venture capitalists and entrepreneurs; evaluating the performance of portfolio managers; asset pricing and more recently exploration of the law and economics of capital market regulation. His work on electronic exchanges in the Journal of Finance won a Smith Breeden Distinguished Paper Prize. He has served as an editor of the Review of Financial Studies, associate editor of the Journal of Finance and serves on several other editorial boards. He has been a consultant for the New York Stock Exchange, Justice Department, and SEC and has served on the NASDAQ Economic Advisory Board. He received his AB from Occidental College (1973) and his Ph.D. in managerial economics from Northwestern University (1980).
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