Simulation of Limit Order Books

如今，大多数电子证券交易所通过限价单（lob）来组织交易，以促进交易活动。限价订单簿是所有未完成的买（卖）限价订单的集中记录，它表明买方（卖方）在给定地点（XETRA，纳斯达克等）以特定价格买入（卖出）特定数量的特定股票的要约。这些订单保留在订单簿中，直到它们被取消或被卖（买）市场订单执行。由于大量的历史限价单数据的可用性，近年来有大量的研究致力于研究限价单的实证方面，调查价格是如何在限价单中形成的，如何预测限价单中的价格变动，以及模拟限价单的方法。所有这些任务都具有复杂的性质，因为许多具有不同目标和不同信息集的异构代理在限制订单簿中相互作用。这就把股票、期货等的限价订单变成了一个复杂的、高维的系统，随着时间的推移而演变，具有重要的动态。本研究项目的目的是开发模型来模拟限价订单数据，再现在真实限价订单中观察到的某些经验性质。这些属性考虑到最终的价格路径、订单形状和订单到达时间，以及非平稳性模式。最终，限价订单是一个反应系统，其中的行动相互影响。从本质上讲，如果一些交易者下了限价单，市场（限价单簿）就会对这一安排做出反应，从而改变LOB的发展。因此，一个“有用的”模型也应该能够真实地模拟限价订单簿的反应，如果订单被放置在该簿中。模拟lob的模型对很多事情都很有用。首先，它们有助于更好地理解各种情况下的金融市场（例如在危机期间）。二是缓解了数据共享问题。第三，尾部事件（危机等）的数据集的丰富有助于使金融算法更加稳健，因为它们可以在比历史数据中可用的更关键的情况下进行测试。点过程、多智能体系统等已被应用于限价单模型，并能够重现限价单中观察到的一些典型特征，但大多数方法缺乏某些维度。最近，机器学习的出现和计算能力的进步使得应用数据驱动的非参数方法来模拟金融数据的规模比以往任何时候都大。尽管缺乏分析可追溯性，但机器学习算法往往比传统模型更灵活。特别是，生成对抗网络（GANs）及其扩展最近被应用于（多变量）时间序列生成。应用生成对抗网络生成限价订单数据的研究还非常有限。该项目旨在开发适合生成限价订单数据的新型GAN架构，例如数量和价格的过程，具有当前文献中缺乏的现实属性。该项目与以下主题一致：(1)人工智能技术，(2)统计与应用概率，(3)非线性系统，(4)运筹学。工业伙伴/合作者是摩根大通。

Most electronic stock exchanges nowadays organize trades via limit order books (LOBs), in order to facilitate trading activity. A limit order book is a centralized record of all outstanding buy (sell) limit orders, which indicate a buyer's (seller's) offer to buy (sell) a specified quantity of a particular stock for a certain price, at a given venue (XETRA, NASDAQ, etc.). These orders remain in the order book until they get either cancelled or executed by a sell (buy) market order.Due to the availability of vasts amounts of historical limit order book data, a lot of research has been devoted in recent years to study empirical aspects of limit order books, investigate how the price is formed within limit order books, how price movements in limit order books may be predicted, as well as methods to simulate limit order books. All those tasks are of complicated nature as many heterogeneous agents with different objectives and different sets of information interact together in limit order books. This turns the limit order book of a stock, future, etc. into a complex, high-dimensional system evolving over time with non-trivial dynamics.The aim of this research project is the development of models to simulate limit order book data which reproduces certain empirical properties observed in real limit order books. These properties regard the resulting price paths, order book shape and order inter-arrival times, as well as non-stationarity patterns. Ultimately, limit order books are responsive systems in which actions affect each other. In essence, if some trader places a limit order, the market (limit order book) reacts to this placement which changes the development of the LOB. Thus, a "useful" model should also be able to simulate the reactions of a limit order book realistically, if an order is placed in the book. Models to simulate LOBs are useful for a variety of things. First of all, they help to better understand financial markets in a variety of scenarios (e.g. during crises). Second, it alleviates issues regarding data sharing. Third, enrichment of data sets from tail events (crises, etc.) can help render financial algorithms more robust, as they can be tested in more critical situations than what is available in historical data.Point processes, multi-agent systems and more have been applied to model limit order books, and are able to reproduce some of the typical characteristics observed in limit order books, but most approaches lack in certain dimensions. Recently, the advent of machine learning and advances in computational power allowed to apply data-driven, non-parametric approaches for the simulation of financial data on a much larger scale than ever before. Despite their lack of analytical tractability, machine learning algorithms tend to be more flexible than conventional models. In particular, generative adversarial networks (GANs) and their extensions have recently been applied to (multivariate) time series generation. The research applying generative adversarial networks to generate limit order book data is yet very limited to. This project aims to develop novel GAN architectures suitable to generate limit order book data, e.g. processes of quantities and prices, with realistic properties which are lacking from the current literature.The project is aligned with the following topics: (1) Artificial intelligence technologies, (2) statistics and applied probability, (3) non-linear systems, (4) operational research.The industrial partner/collaborator is J.P.Morgan.