A law of large numbers for limit order books
Mathematical Finance
2015-01-06 v1 Trading and Market Microstructure
Abstract
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a limit theorem. The limit theorem states that, given regularity conditions on the random order flow, the key quantities converge in probability to a tractable continuous limiting model. In the limit model the buy and sell volume densities are given as the unique solution to first-order linear hyperbolic PDEs, specified by the expected order flow parameters.
Keywords
Cite
@article{arxiv.1501.00843,
title = {A law of large numbers for limit order books},
author = {Ulrich Horst and Michael Paulsen},
journal= {arXiv preprint arXiv:1501.00843},
year = {2015}
}