Mathematical and data-driven modelling of multi-asset markets
Lead Research Organisation:
University of Oxford
Abstract
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.
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.
Planned Impact
Probabilistic modelling permeates the Financial services, healthcare, technology and other Service industries crucial to the UK's continuing social and economic prosperity, which are major users of stochastic algorithms for data analysis, simulation, systems design and optimisation. There is a major and growing skills shortage of experts in this area, and the success of the UK in addressing this shortage in cross-disciplinary research and industry expertise in computing, analytics and finance will directly impact the international competitiveness of UK companies and the quality of services delivered by government institutions.
By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to
- sharpening the UK's research lead in this area and
- meeting the needs of industry across the technology, finance, government and healthcare sectors
MATHEMATICS, THEORETICAL PHYSICS and MATHEMATICAL BIOLOGY
The explosion of novel research areas in stochastic analysis requires the training of young researchers capable of facing the new scientific challenges and maintaining the UK's lead in this area. The partners are at the forefront of many recent developments and ideally positioned to successfully train the next generation of UK scientists for tackling these exciting challenges.
The theory of regularity structures, pioneered by Hairer (Imperial), has generated a ground-breaking approach to singular stochastic partial differential equations (SPDEs) and opened the way to solve longstanding problems in physics of random interface growth and quantum field theory, spearheaded by Hairer's group at Imperial. The theory of rough paths, initiated by TJ Lyons (Oxford), is undergoing a renewal spurred by applications in Data Science and systems control, led by the Oxford group in conjunction with Cass (Imperial). Pathwise methods and infinite dimensional methods in stochastic analysis with applications to robust modelling in finance and control have been developed by both groups.
Applications of probabilistic modelling in population genetics, mathematical ecology and precision healthcare, are active areas in which our groups have recognized expertise.
FINANCIAL SERVICES and GOVERNMENT
The large-scale computerisation of financial markets and retail finance and the advent of massive financial data sets are radically changing the landscape of financial services, requiring new profiles of experts with strong analytical and computing skills as well as familiarity with Big Data analysis and data-driven modelling, not matched by current MSc and PhD programs. Financial regulators (Bank of England, FCA, ECB) are investing in analytics and modelling to face this challenge. We will develop a novel training and research agenda adapted to these needs by leveraging the considerable expertise of our teams in quantitative modelling in finance and our extensive experience in partnerships with the financial institutions and regulators.
DATA SCIENCE:
Probabilistic algorithms, such as Stochastic gradient descent and Monte Carlo Tree Search, underlie the impressive achievements of Deep Learning methods. Stochastic control provides the theoretical framework for understanding and designing Reinforcement Learning algorithms. Deeper understanding of these algorithms can pave the way to designing improved algorithms with higher predictability and 'explainable' results, crucial for applications.
We will train experts who can blend a deeper understanding of algorithms with knowledge of the application at hand to go beyond pure data analysis and develop data-driven models and decision aid tools
There is a high demand for such expertise in technology, healthcare and finance sectors and great enthusiasm from our industry partners. Knowledge transfer will be enhanced through internships, co-funded studentships and paths to entrepreneurs
By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to
- sharpening the UK's research lead in this area and
- meeting the needs of industry across the technology, finance, government and healthcare sectors
MATHEMATICS, THEORETICAL PHYSICS and MATHEMATICAL BIOLOGY
The explosion of novel research areas in stochastic analysis requires the training of young researchers capable of facing the new scientific challenges and maintaining the UK's lead in this area. The partners are at the forefront of many recent developments and ideally positioned to successfully train the next generation of UK scientists for tackling these exciting challenges.
The theory of regularity structures, pioneered by Hairer (Imperial), has generated a ground-breaking approach to singular stochastic partial differential equations (SPDEs) and opened the way to solve longstanding problems in physics of random interface growth and quantum field theory, spearheaded by Hairer's group at Imperial. The theory of rough paths, initiated by TJ Lyons (Oxford), is undergoing a renewal spurred by applications in Data Science and systems control, led by the Oxford group in conjunction with Cass (Imperial). Pathwise methods and infinite dimensional methods in stochastic analysis with applications to robust modelling in finance and control have been developed by both groups.
Applications of probabilistic modelling in population genetics, mathematical ecology and precision healthcare, are active areas in which our groups have recognized expertise.
FINANCIAL SERVICES and GOVERNMENT
The large-scale computerisation of financial markets and retail finance and the advent of massive financial data sets are radically changing the landscape of financial services, requiring new profiles of experts with strong analytical and computing skills as well as familiarity with Big Data analysis and data-driven modelling, not matched by current MSc and PhD programs. Financial regulators (Bank of England, FCA, ECB) are investing in analytics and modelling to face this challenge. We will develop a novel training and research agenda adapted to these needs by leveraging the considerable expertise of our teams in quantitative modelling in finance and our extensive experience in partnerships with the financial institutions and regulators.
DATA SCIENCE:
Probabilistic algorithms, such as Stochastic gradient descent and Monte Carlo Tree Search, underlie the impressive achievements of Deep Learning methods. Stochastic control provides the theoretical framework for understanding and designing Reinforcement Learning algorithms. Deeper understanding of these algorithms can pave the way to designing improved algorithms with higher predictability and 'explainable' results, crucial for applications.
We will train experts who can blend a deeper understanding of algorithms with knowledge of the application at hand to go beyond pure data analysis and develop data-driven models and decision aid tools
There is a high demand for such expertise in technology, healthcare and finance sectors and great enthusiasm from our industry partners. Knowledge transfer will be enhanced through internships, co-funded studentships and paths to entrepreneurs
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/S023925/1 | 01/04/2019 | 30/09/2027 | |||
| 2596025 | Studentship | EP/S023925/1 | 01/10/2021 | 30/09/2025 | Milena Vuletic |