论文标题
订单簿动力和流动性波动：限制定理和大偏差
Order book dynamics with liquidity fluctuations: limit theorems and large deviations
论文作者
论文摘要
我们为具有不同类型的液体类型的限制顺序簿动力学的动力学提出了一类随机模型。在这类模型中，我们研究了一个差异均匀减少的模型，属于被称为人口过程的过程类别，具有统一的灾难。大量（LLN），中心极限定理（CLT）和大偏差（LD）的定律证明了我们的灾难均匀灾难的模型。我们的结果使我们能够令人满意地解释价格的波动性和本地趋势，以及在这种类型的市场中观察到的相关经验特征。此外，它向我们展示了这些局部趋势和波动率如何取决于Bid-ask扩散的典型值。此外，我们使用我们的模型来展示利差和价格中发生的大偏差，例如在Flash崩溃中观察到的偏差。
We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.
