A Law of Large Numbers for Limit Order Books

• 成果类型: Article
• 署名作者: Horst, Ulrich; Paulsen, Michael
• 署名单位: Humboldt University of Berlin
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0848
• 发表日期: 2017
• 页码: 1280-1312
• 关键词: price dynamics; MARKET; MODEL

摘要

We define a stochastic model of a two-sided limit order book in terms of its key quantities best bid [ask] price and the 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. We calibrate order flow dynamics to market data for selected stocks and show how our model can be used to derive endogenous shape functions for models of optimal portfolio liquidation under market impact. Funding: