ASSESSING THE PERFORMANCE OF AN INTER-MARKET TRADING STRATEGY IN THE LOW AND HIGH FREQUENCY DOMAIN BASED ON HISTORIC DATA USING MACHINE LEARNING

深度学习概念的有趣应用和扩展应该在博士研究中开创先河，将它们应用于高频订单簿数据，即使用机器学习工具来推导高频交易机制。在我攻读算法交易硕士学位期间的课程学习中，我评估了NVWAP(名义成交量加权平均价格)曲线受四个统计量的支配，即陡化/平化和收缩/扩张。NVWAP曲线的收缩/扩张是通过计算限价指令的买入方和卖出方的总成交量变化来量化的。这一概念应该作为输入，并由机器学习工具进一步发展，以推导出自动化交易系统在实践中是否可以有利可图地运行。要做到这一点，数据应该被分成不同的块，作为深层神经网络的输入。然后，它的发现应该应用于实时交易市场，并评估是否可以实现有利可图的运营。为了评估市场间的关系，可以同时调查两个或更多相关资产，以得出交易决策。与金融和投资的概念相比，机器学习的科学是相当新的。鉴于最近在已记录和可访问的数据量以及现代计算技术方面的发展，有必要寻找这两个主题之间的协同效应，并扫描数据，寻找以前对市场参与者来说不明显的模式。显然，这是一项具有挑战性的任务，因为大型投行等实力雄厚的参与者，以及机构和专业投资者的目标也是如此。最近在结合先进计算工具和金融方面取得的重大进展进一步推动了这一点。机器学习技术没有魔力；然而，它能够学习过去的数据模式，以便在未来应用其发现。基于机器学习的一般定义是关于某一类任务T和性能度量P从经验E学习的计算机程序，如果它在T中的任务中的性能(由P测量)随着经验E的改进，则该任务将被调查。机器学习中最新的工具之一是深度神经网络(DNN)。深度神经网络(DNN)是一种在输入层和输出层之间具有多个隐层单元的人工神经网络。例如，人们可以使用超过1.2亿个优质和次级抵押贷款的数据集来构建用于建模抵押贷款拖欠和提前还款风险的深度神经网络，并模拟抵押贷款17个投资组合以用于风险分析。甚至有人发现，金融学中的一些经典理论，如有效市场假说，可能会受到深度学习的挑战。另一个动机是应用深度学习来发现尚未在市场上执行的交易策略。为此，历史数据被分成两个组成部分。首先，将80%的历史数据定义为测试数据，即调查市场结构的数据。剩下的20%是训练数据，即神经网络以前从未见过的数据。换句话说，80%的数据的学习结果现在应用于剩余的20%的数据，结果是几种金融工具确实可以进行有利可图的交易。

An interesting application and expansion of the deep learning concepts should be pioneered in PhD research by applying them to high frequency order book data, namely to use machine learning tools to derive a high frequency trading mechanism. As researched in coursework during my MSc in Algorithmic Trading, I evaluated that NVWAP (Notional Volume Weighted Average Price) curves are governed by four statistics, namely steepening/flattening and contraction/expansion. Contraction/expansion of NVWAP curves is quantified by computing the change in total volume on both, the bid and ask-side of the limit order book. This concept should be taken as input and further developed by machine learning tools to derive whether an automated trading system could operate profitably in practice. To do this, the data is supposed to be separated in various chunks serving as input for the deep neural net. Its findings should then be applied on trading real time markets and evaluated whether a profitable operation is achievable. To appreciate inter-market relations, two or more correlated assets can be investigated simultaneously to derive trading decisions. The science of machine learning is quite new compared to the concepts of finance and investments. Given recent developments in terms of the amount of data recorded and being accessible, and modern computing technology, it is worthwhile to search for synergy between the two subjects and scan the data for patterns that have not been obvious for market participants before. Clearly, this is a challenging task since powerful players such as large investment banks, but also institutional and professional investors aim at doing the same. Recent and major advances in combining advanced computational tools and finance further motivate to do so. There is no magic in machine learning technique; however, it is capable of learning patterns of data from the past to apply its findings in future. Grounded on the general definition of machine learning to be a computer program learning from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E, the task will be investigated. One of the most recent tools in machine learning are deep neural nets (DNN). A deep neural network (DNN) is an artificial neural network with multiple hidden layers of units between the input and output layers. For example, one can built deep neural networks for modeling mortgage delinquency and prepayment risk using a dataset of over 120 million prime and subprime mortgages and simulate mortgage 17 portfolios for risk analysis purposes. It was even found that some of the classical theory in finance such as the efficient market hypothesis might be challenged by deep learning. Yet another motivation is to apply deep learning to discover trading strategies not yet executed in the markets. To do so, the historic data was split up into two constituent parts. Firstly, 80% of the historic data were defined to be test data, i.e. data on which the market structure was investigated. The remaining 20% were training data, i.e. data the neural net has not seen before. In other words, the learning outcomes of 80% of the data were now applied to the remaining 20% of the data with the result that several financial instruments could indeed be profitably traded.