Rough Volatility: A Trojan horse into modern Financial computing

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.

Volatility modelling is at the very core of financial markets, whether Equity, Foreign Exchange or Fixed Income. The latter has benefited from an early consensus on a given model, that has become predominant. This has not been the case in the Equity and FX worlds, and each institution has been using variants of many different volatility models. One particular, and dangerous, issue has been the misalignment between models used by the front office for pricing and by risk management, both acting under different measures. Our proposed research, based on years of experience understanding models and data, is to develop a unified model able to capture the specificities of the market and to reconcile these two sides. This will not only allow for better estimation and calibration, but will also simplify IT systems by reducing a plethora of models to one, thereby limiting model risks and industrial costs. It will further make it simpler for the regulator (Bank of England and the Financial Conduct Authority in the UK) to set up a safer regulatory environment for trading. In order to make this possible, we will interact actively with the financial industry to promote our research outputs, both through Practitioners' conferences (QuantMinds in particular) and by publishing in industry-oriented journals (Risk Magazine).

Open-source code and research has recently greatly benefited from IPython notebook environment coded in Python through the online Github platform. It has in particular made it easier for users to apply directly new research developments without the burden of starting from scratch. In our view, this has accelerated the pace of new results and the expansion of the community working on this. We therefore plan to make all our results publicly available through such avenues, thereby facilitating access to any users. Interdisciplinarity comes at the (very low) cost of allowing users to directly test our results without necessarily understanding the theoretical contents. The PI has strong coding experience---academic and industrial--in Python and, given the scope of the project, there is no doubt that a patented software shall arise from it.

The PI has been running one of the most successful MSc in Mathematics and Finance programme in Europe for the past four years, and has in particular endeavoured to develop its data and practical contents without compromising its mathematical quality and rigour. This in particular implies making part of the PI's (and other staff members') research accessible to students, who will become leaders in tomorrow's Finance community. By integrating part of the research output, through examples, projects, data experiments, in the MSc curriculum (which already includes elements of rough volatility, Machine Learning, and Computing), students, and thus future generations, will thus grow accustomed to this new paradigm and new tools, and will spread them in their future endeavours.