# Modeling of limit order books by particle methods and dimensional analysis

The subject of this talk is an approach to modeling the tick-by-tick dynamics of the limit order trading mechanism based on particle methods and dimensional analysis.

We will illustrate an application of the master equation solution concept for the distribution of limit orders within the limit order book and in general the modeling of limit order markets using particle methods.

Following that we will illustrate the use of dimension analysis (of the style, for example, used to calculate the period of a pendulum) to make predictions about aggregate quantities of market trading such as spread, volatility and market impact. We verify these predictions against trading data from the London Stock Exchange and show very good predictive power.

### Bibliography

The power of patience; A behavioral regularity in limit order placement

I. Zovko and J. D. Farmer

Quantitative Finance 2 387-392 (2002)

Statistical theory of the continuous double auction

E. Smith and J. D. Farmer and L. Gillemot and S. Krishnamurthy

Quantitative Finance 3 481-514 (2003)

The predictive power of zero intelligence in financial markets

J. D. Farmer and P. Patelli and I. Zovko

Proceedings of the National Academy of Sciences of the United States of America 102

2254-9 (2005)

Slides (PDF, 2.61 MB)

Back to the program