A law of large numbers for limit order books

Ulrich Horst and Michael Paulsen

Papers from arXiv.org

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.

Date: 2015-01
New Economics Papers: this item is included in nep-mst
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Citations: View citations in EconPapers (4)

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