英文标题：
《The order book as a queueing system: average depth and influence of the
size of limit orders》
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作者：
Ioane Muni Toke
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最新提交年份：
2013
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英文摘要：
We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic results for birth-and-death processes, we build an analytical formula for the shape (depth) of a continuous order book model which is both founded by market mechanisms and very close to empirically tested formulas. We relate this shape to the probability of execution of a limit order, highlighting a law of conservation of the flows of orders in an order book. We then extend our model by allowing random sizes of limit orders, hereby allowing to study the relationship between the size of the incoming limit orders and the shape of the order book. Our theoretical model shows that, for a given total volume of incoming limit orders, the less limit orders are submitted (i.e. the larger the average size of these limit orders), the deeper is the order book around the spread. This theoretical relationship is finally empirically tested on several stocks traded on the Paris stock exchange.
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中文摘要：
我们研究了一个单边订单簿模型的分析性质，其中限额订单和市场订单的流动是泊松过程，取消订单的寿命分布是指数分布。尽管过于简单，但该模型提供了一种不应忽视的分析可处理性。利用生灭过程的基本结果，我们建立了一个连续订单簿模型形状（深度）的分析公式，该模型由市场机制建立，并且非常接近经经验检验的公式。我们将此形状与执行限制订单的概率联系起来，强调订单簿中订单流的守恒定律。然后，我们通过允许限额订单的随机大小来扩展我们的模型，从而允许研究传入限额订单的大小与订单簿形状之间的关系。我们的理论模型表明，对于给定的总进货限额订单，提交的限额订单越少（即这些限额订单的平均规模越大），价差周围的订单簿就越深。这种理论关系最终在巴黎证券交易所交易的几只股票上进行了实证检验。
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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：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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