Working title: Applications of machine learning to financial risk management

该项目旨在将机器学习方法应用于金融领域的问题。随着计算能力的提高和对不断增加的数据量的访问，机器学习方法已经开始对量化金融领域产生重大影响，使交易员和风险经理能够解决以前难以解决的问题，并使日常任务大规模自动化。随着机器学习应用的增加，我们同样面临着许多可能适用于这些方法的开放问题，特别是深度学习方法的使用引入了关于算法的可解释性、健壮性和效率的问题。这个项目属于EPSRC数学科学研究领域。这个博士项目的总体目标是开发新的机器学习方法，以期将其应用于衍生品定价和套期保值。金融业面临的一个常见问题是，如何通过构建对冲工具组合来管理风险。现代量化金融为交易员提供了一种有效的工具，可以在完全市场和零市场摩擦的理想化假设下，以最佳方式构建这样的投资组合。当这些假设不成立时，经典的方法可能会崩溃，促使研究人员通过深度强化学习等方法来研究无模型对冲。这些新方法的一个主要限制是无法获得用于训练算法的真实市场数据。众所周知，神经网络需要大量的训练数据才能达到全局最优，但在场外衍生品的情况下，可用的有用现实数据量是有限的。例如，在十年的时间里，使用每日数据，我们只能得到几千个样本来训练我们的模型。这一限制促使我们需要一个有效的市场模拟器，通过它我们可以为我们的套期保值代理生成训练数据。当然，经典的量化金融有各种各样的市场参数模型，如连续时间半鞅模型、局部波动率模型和随机波动率模型。然而，众所周知，这些模型很难适应真实世界的数据，并依赖于重大的建模假设，因此，在这些路径上训练的深度对冲代理在利用真实世界数据进行实时交易时，可能表现不佳。相反，人们对使用产生式机器学习方法进行市场的无模型模拟产生了一些兴趣，并在使用神经网络进行市场模拟方面取得了一些进展。然而，当前最先进的市场生成器在用于培训对冲机构时存在一些问题。特别是，产生的路径表现出漂移，这使得交易代理能够找到统计套利策略--这些策略平均产生正回报--而不是通过对冲来执行适当的风险管理。因此，这个博士项目的一个重点是研究可以应用于消除市场生产者的统计套利并更好地解释市场未来状态的不确定性的方法。该项目的结果将是管理金融风险的新方法，与现有方法相比，这些方法对假设和特定模型的依赖程度更低。因此，他们对未来不断变化的世界状况将更加健壮和有弹性。该项目是与摩根大通银行合作进行的，自2020年2月以来，我一直在摩根大通银行兼职，每周工作一天。

The project aims to apply machine learning methods to problems within finance. With the advent of increased computational capacity and access to ever increasing volumes of data, machine learning methods have begun to make significant impact on the domain of quantitative finance, enabling traders and risk managers to solve previously intractable problems, and automate routine tasks at large scale. As applications of machine learning increase, we are equally faced with the a number of open problems which may be amenable to these methods, and further, the use of deep learning methods in particular introduces questions regarding the explainability, robustness and efficiency of algorithms. This project falls within the EPSRC Mathematical Sciences research area.The overarching aim of this PhD project is to develop novel machine learning methodology with a view to applying it in derivatives pricing and hedging. A common problem faced in finance is that of managing risk through the construction of a portfolio of hedging instruments. Modern quantitative finance has equipped the trader with an effective toolkit in which to optimally construct such a portfolio, under the idealised assumptions of complete markets and zero market frictions. When these assumptions do not hold, the classical methods may break down, prompting researchers to investigate model-free hedging through methods such as deep reinforcement learning. A major limitation of these new approaches is the availability of real market data on which to train the algorithms. It is well known that neural networks require vast quantities of training data in order to reach global optima, but in the case of over-the-counter derivatives, the amount of useful real-life data available is limited. For example, over a ten-year period, with daily data, we would arrive at only a few thousand samples on which to train our models. This limitation motivates the need for an effective market simulator, through which we may generate training data for our hedging agent. Of course, classical quantitative finance has a wide array of parametric models for markets, such as continuous time semi-martingale models, local volatility models, and stochastic volatility models. However, these models are notoriously difficult to fit to real-world data and rely on significant modelling assumptions, so that a deep hedging agent trained on these paths is likely to perform poorly when put into live trading on real world data. Instead, there has been some interest in model-free simulation of markets using generative machine learning methods, and some progress has been made into market simulation using neural networks. However, there are some issues with the current state-of-the-art market generators, when used to train the hedging agent. In particular, the paths generated exhibit drifts which permit the trading agent to find statistical arbitrage strategies - ones which on average produce a positive payoff - rather than performing proper risk management through hedging. Thus, a focus for this PhD project is to investigate methods which can be applied to remove statistical arbitrage from the market generator and better account for uncertainty about the future state of markets.The outcomes for this project will be new methodologies for managing financial risk that rely less on assumptions and specific models, than current methods. Therefore, they will be more robust and resilient to changing states of the world in the future.This project is being undertaken in collaboration with JPMorgan Chase Bank, where I have been working on a part-time, one day per week basis, since February 2020.