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摘要翻译：
我们提出了一个模型，在一个流动的市场中，买进和卖出订单是以高频率提交的，限价订单书的动力学。我们导出了一个关于出价和出价排队联合动力学的泛函中心极限定理，并证明了当订单到达频率较大时，极限订单书的日内动力学可以近似为一个马尔可夫跳扩散过程，该过程的特征可以用潜在订单流的统计性质来明确描述。这一结果使人们能够对各种有兴趣的量，如价格上涨的概率或直到下一次价格变动的持续时间的分布，得到易于处理的解析近似，条件是订单书的状态。我们的结果允许订单流中广泛的分布假设和时间依赖性，并适用于为订单书动力学提出的广泛的随机模型，包括基于泊松点过程的模型、自激点过程的模型和ACD-GARCH族模型。
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英文标题：
《Order book dynamics in liquid markets: limit theorems and diffusion
approximations》
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作者：
Rama Cont and Adrien De Larrard
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最新提交年份：
2012
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the limit order book may be approximated by a Markovian jump-diffusion process in the positive orthant, whose characteristics are explicitly described in terms of the statistical properties of the underlying order flow. This result allows to obtain tractable analytical approximations for various quantities of interest, such as the probability of a price increase or the distribution of the duration until the next price move, conditional on the state of the order book. Our results allow for a wide range of distributional assumptions and temporal dependence in the order flow and apply to a wide class of stochastic models proposed for order book dynamics, including models based on Poisson point processes, self-exciting point processes and models of the ACD-GARCH family.
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PDF链接：
https://arxiv.org/pdf/1202.6412
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