Simulation of Limit Order Books

如今，大多数电子证券交易所都通过限价订单(LOB)来组织交易，以促进交易活动。限价订单账簿是所有未完成的买入(卖出)限价订单的集中记录，这些订单表明买家(卖家)提出在给定的地点(Xetra、NASDAQ等)以特定的价格购买(出售)特定数量的特定股票。由于有大量的历史限价订单数据可用，近年来人们致力于研究限价订单账簿的经验方面，调查限价订单账簿内的价格是如何形成的，如何预测限价订单账簿中的价格变动，以及模拟限价订单账簿的方法。所有这些任务都是复杂的，因为许多具有不同目标和不同信息集的异类代理在限制订单簿中相互作用。这使得股票、期货等的限价指令账簿变成了一个随时间演化的具有非平凡动态的复杂的高维系统。本研究项目的目的是建立模型来模拟限价指令账簿数据，该模型再现了在真实的限价指令账簿中观察到的某些经验性质。这些属性涉及最终的价格路径、订单簿形状和订单到达间隔时间，以及非平稳模式。归根结底，限价指令簿是反应迅速的系统，其中的操作相互影响。本质上，如果某个交易者下了限价指令，市场(限价指令)就会对这种改变LOB发展的配售做出反应。因此，一个“有用的”模型也应该能够真实地模拟限价指令书的反应，如果在书中下了订单的话。模拟LOB的模型对于各种事情都很有用。首先，它们有助于更好地了解各种情况下的金融市场(例如在危机期间)。其次，它缓解了有关数据共享的问题。第三，丰富尾部事件(危机等)的数据集可以帮助使金融算法更加稳健，因为它们可以在比历史数据可用的更关键的情况下进行测试。点过程、多代理系统等已被应用于限制订单账簿的模型，并能够再现限制订单账簿中观察到的一些典型特征，但大多数方法在某些维度上缺乏。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得多。尽管机器学习算法缺乏分析处理能力，但它们往往比传统模型更灵活。特别是，生成性对抗网络(GANS)及其扩展最近已被应用于(多变量)时间序列的生成。应用产生式对抗性网络生成限价指令账簿数据的研究还非常有限。该项目旨在开发适合生成限量订单账簿数据的新型GaN体系结构，例如数量和价格的过程，具有当前文献所缺乏的真实性质。该项目与以下主题相一致：(1)人工智能技术，(2)统计和应用概率，(3)非线性系统，(4)运筹学研究。

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.