Rough Volatility: A Trojan horse into modern Financial computing

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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.