Rough Volatility: A Trojan horse into modern Financial computing

金融部门是当今社会的一个关键行业，为其提供正确准确的工具，同时管理风险，对于防止以前的灾难再次发生至关重要。英格兰银行和金融行为监管局最近（2019年10月16日）的一项审查强调了基于机器学习的新方法在金融相关公司中的重要性（并且已经大量存在）。新技术需要新人，或者至少需要一套新技能。这项提议的目标是开发一套新的工具，用更精确的模型更新以前的模型，利用现代技术利用不断增长的计算能力。我们的目标是开发一套模型（称为“粗略波动率”），能够捕捉股票价格的历史行为，同时与未来预测和期权数据保持一致。尽管这个问题的性质很明显，但它仍然是开放的，最近的事态发展为可能的解决办法铺平了道路。因此，第一个目标是建立一个与实际数据一致的健壮的统一模型，并监控相应的潜在风险。第二个目标是开发数字技术，使金融机构和监管机构能够充分利用和管理这一模型。这个数值部分是该项目的核心要素，将基于经典概率工具和现代机器学习技术的结合。该项目的最后一步是展示量子计算方法（目前主要在理论上可用）如何帮助加快这些计算，从而为量化金融的未来打开许多新的大门。我们的结果的明显好处将是提供一个对社会产生深远影响的大型行业，提供可以监控的精确和准确的工具，从而降低相关风险。它还将弥合“粗波动率”领域的许多现有差距，并在经典数学金融与现代数量金融之间建立许多新的联系；因此，这种新的粗糙波动率范式将构成一个开发现代金融模型计算技术的平台。虽然我们的项目显然深深扎根于金融领域，但我们的研究结果不仅将为一些深度学习和量子算法提供测试用例，还将有助于阐明这些新工具如何以及应该如何以受控的方式应用。由于机器学习现在在日常生活的许多领域无处不在，我们的项目将使该领域更加强大，更容易和广泛地访问。

The Financial sector is a key industry in our current society, and providing it with the right accurate tools, while managing the risks, is of paramount importance in order to prevent previous disasters to occur again. A recent (16 October 2019) review by the Bank of England and the Financial Conduct Authority emphasised the importance (and already large) presence of new methods based on Machine Learning in finance-related firms. New techniques require new people or, at the very least new sets of skills. The goal of this proposal is to develop a new set of tools, updating former models with more accurate ones, with modern technologies harnessing the ever-increasing computational power available.We aim at developing a set of models (called `rough volatility') able to capture the historical behaviour of stock prices while being consistent with future forecasts and options data. Despite the obvious nature of the problem, it is still open, and recent developments have paved the way to potential solutions. The first goal is therefore to build a robust unified model consistent with real data, as well to as monitor the corresponding potential risks. The second goal is to develop the numerical techniques required to make this model fully accessible and manageable by financial institutions and the regulators. This numerical part is a core element of the project, and will be based on a combination of classical probabilistic tools and modern Machine Learning techniques. The final step of the project is to show how methods from quantum computing---so far mainly available theoretically---can help speed up these computations, and thereby open up many new doors for the future of Quantitative Finance.The obvious benefits of our results will be to provide a large industry, with deep impact on society, with precise and accurate tools that can be monitored, and hence whose associated risks are reduced. It will also bridge many existing gaps in the field of `rough volatility', as well as build many new connections between classical Mathematical Finance and modern Quantitative Finance; this new rough volatility paradigm will thus constitute a platform to develop modern computing techniques for financial models. Though our project is obviously deeply anchored in Finance, our results will not only provide test cases for some Deep Learning and quantum algorithm, but will also help clarify how these new tools can and should be applied in a controlled way. Since Machine Learning is now ubiquitous in many areas of everyday life, our project will make the field more robust and easily and widely accessible.