Diffusion Scaling of a Limit-order Book Model
Steven E. Shreve, Carnegie Mellon University, United States
Date:
11 Sep 2014
Time:
4.00pm – 5.30pm
Venue:
Hon Sui Sen Auditorium NUS Business School
(This seminar is organized jointly with the Risk Management Institute and NUS Finance & Risk Management Cluster)
About the Speaker
Steven Shreve is the Orion Hoch University Professor of Mathematics at Carnegie Mellon University, where he co-founded Carnegie Mellon’s Master’s degree in Computational Finance, now in its 20th year, with campuses in New York and Pittsburgh. Shreve received an MS in electrical engineering and a PhD in mathematics from the University of Illinois. Shreve has also been a faculty member of the University of California at Berkeley and Massachusetts Institute of Technology. Shreve’s book “Stochastic Calculus for Finance” won the 2004 Wilmott award for “Best New Book in Quantitative Finance.” Shreve is co-author of the books “Brownian Motion and Stochastic Calculus” and “Methods of Mathematical Finance,”advisory editor of the journal “Finance and Stochastics,” and past-President of the Bachelier Finance Society. He has published over forty articles in scientific journals on stochastic calculus, stochastic control, and the application of these subjects to finance, including the effect of transaction costs on option pricing, the effect of unknown volatility on option prices, pricing and hedging of exotic options, and models of credit risk.
Abstract
With the movement of trading away from the trading floor onto electronic exchanges – and the accompanying rise in the volume of order submission – has come an increase in the need for tractable mathematical models of the whole limit order book. The problem is inherently high-dimensional and the most natural description of the dynamics of the order flows has them depend on the state of the book in a discontinuous way. We examine a popular discrete model from the literature and describe its limit under a diffusion scaling inspired by queueing theory. Interesting features include a process that is either “frozen” or diffusing according to whether another diffusion is positive or negative. This is joint work with Christopher Almost and John Lehoczky.
