Mathematical and data-driven modelling of multi-asset markets

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While the bulk of mathematical models in finance has focused on detailed analytical models of single-asset markets, the majority of applications are concerned with multi-asset markets, often with a large number of assets. This leads to many theoretical and computational challenges related to scalability, model sparsity, and arbitrage constraints. The aim of this research project is to develop efficient analytical and data-driven modelling approaches and algorithms for multi-asset financial markets which are scalable to high-dimensional settings. The research project will focus on four directions: 1. Development of arbitrage-free simulation methods for options markets. 2. Analysis and risk monitoring of multi-asset trading strategies. 3. Microstructural modelling of multi-asset markets. 4. Data-driven approaches for hedging and risk management. Our methodology will combine analytical methods and stochastic modelling with data-driven approaches based on the use of novel computational methods such as Generative adversarial networks (GAN) [1] and the Signature method [3] to tackle these problems. This research project addresses various challenges faced by financial institutions, risk managers, and market regulators. Special attention will be devoted to algorithmic and implementation aspects, and case studies using market data. Applications will focus on the analysis and simulation of strategies involving options and other volatility contracts [4]. The project is aligned with the following EPSRC research areas: (1) machine learning, deep learning, and data-centric modelling (2) statistics and applied probability, (3) mathematical modelling, (4) operational research. This project will be done in partnership with BNP Paribas. [1] Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. "Generative adversarial networks." Communications of the ACM 63, no. 11 (2020): 139-144. [2] Buehler, Hans, Lukas Gonon, Josef Teichmann, and Ben Wood. "Deep hedging." Quantitative Finance 19, no. 8 (2019): 1271-1291. [3] Gyurkó, L. G., Lyons, T., Kontkowski, M., & Field, J. (2013). Extracting information from the signature of a financial data stream. arXiv preprint arXiv:1307.7244. [4] Cont, Rama, and José Da Fonseca. "Dynamics of implied volatility surfaces." Quantitative finance 2, no. 1 (2002): 45.