Research in Mathematical & Computational Finance

The Oxford Mathematical and Computational Finance Group is one of the leading academic research groups  in the world focused on mathematical modeling in finance and offers a thriving research environment, with experts covering multiple  areas of quantitative finance. Our group maintains close links with the Data Science, Stochastic Analysis and Numerical Analysis groups as well as the Institute for New Economic Thinking (INET), the Alan Turing Institute (Machine Learning in Finance), DataSig, the Oxford-Man Institute of Quantitative Finance and the Oxford Probability Group,  enabling cross-fertilisation of ideas and techniques.

Research activities of the group cover a wide spectrum of topics in Quantitative Finance, ranging from  market microstructure and high-frequency modeling  to macro-financial modeling and systemic risk, as well as more traditional topics such as  portfolio optimisation, derivative pricing, credit risk modeling, using a variety of methods: stochastic analysis, probability, partial differential equations, optimisation, numerical simulation, statistics and machine learning.

Mathematical Foundations and Continuous-time finance

Positioned within Oxford's Mathematical Institute, the group has developed a unique expertise in the mathematical foundations underlying quantitative finance and pioneered new approaches in mathematical modeling.

Sam Cohen, Rama Cont, Ben Hambly, Blanka Horvath, Jan Obloj and Zhongmin Qian explore topics in stochastic analysis  -stochastic calculus, backward stochastic differential equations, interacting particle systems, Malliavin calculus, Functional Ito calculus, rough path theory, pathwise methods in stochastic analysis, optimal transport- and their applications to the design of robust models for the pricing and hedging of derivatives in presence of model uncertainty. 
Michael Monoyios works on duality methods for optimal investment and consumption problems, and on valuation and hedging problems in incomplete markets. He has worked on models with transaction costs, and with partial and inside information on asset price evolution. He has interests in Fernholz's stochastic portfolio theory, and on the geometric interpretation of functionally generated portfolios that arise in this theory. 
Jan Obloj works on robust formulations of classical problems -- pricing, hedging, risk management, optimal investment – and seeks to understand and quantify the effects of model uncertainty.
Blanka Horvath focusses on implied volatility modelling, rough volatility models, stochastic volterra equations and stochastic volatility models their short -time asymptotic properties as well as their numerical properties for pricing, hedging and simulation.

Statistical modeling and Machine Learning in Finance

Our group is one of the few academic research teams in the world with an active research agenda at the interface of machine learning and quantitative finance. Several group members are Fellows of the Alan Turing Institute.

Hanqing Jin is Director of the Oxford-Nie Big Data Lab, where Ning Wang has developed algorithms for sentiment analysis based on social media data.
Sam Cohen is exploring applications of Deep Learning  to continuous-time finance as well as issues related to model robustness and its interaction with statistical modelling and optimal control.
Rama Cont, Blanka Horvath and Justin Sirignano investigate the use of Deep Learning and  data-driven modelling in finance.
Terry Lyons and his team investigate the use of rough path signatures for machine learning.
Jan Obloj employs tools from the optimal transport theory to develop data-driven estimators for risk measures, and to quantify robustness of deep neural networks to adversarial attacks.
Blanka Horvath develops deep learning tools for option pricing, (deep) calibration and hedging and for data-driven simulation of asset price dynamics and data-driven portfolio choice problems.

Market microstructure and algorithmic finance

Álvaro Cartea  focuses on mathematical models of algorithmic trading and  the design of optimal trade execition strategies in electronic markets.

Rama Cont pioneered the analytical study of stochastic models for limit order books and intraday market modeling, and investigates the impact of algorithmic trading on market stability and liquidity.

Leandro Sanchez-Betancourt studies the equilibrium between makers and takers of liquidity with continuous-time models and tools from stochastic control and machine learning.

Macro-financial modeling: financial stability and systemic risk

Our group is actively engaged in the development of mathematical models of large-scale financial systems with the goal of providing quantitative insights on financial stability and systemic risk to regulators and policy makers.
Rama Cont and Ben Hambly  investigate the link between micro- and macro-behavior in stochastic models of direct and indirect contagion in financial markets, using network models and analogies with interacting particle systems.

Rama Cont,Research Fellow at the  Institute for New Economic Thinking (INET), have developed network models and simulation-based approaches for macro stress-testing and monitoring systemic risk in banking systems, in liaison with central banks and international organisations such as the Bank of England, the European Central Bank, IMF and Norges Bank.

Rama Cont is  Director of the Oxford Martin Programme on Systemic Resilience, an interdisciplinary programme aimed at exploring solutions for managing stress scenarios with the potential for major and prolonged economic disruption, severe human or economic impacts, and contagion. 

Computational Finance

Our group is a leader in the development of advanced numerical methods and  high performance computiing for high-dimensional problems in finance:
Mike Giles is a pioneer  on multilevel Monte-Carlo methods and their applications in finance, and a leading expert on the use of GPU and high performance computing methods in finance.
Raphael Hauser has developed robust numerical methods for portfolio optimisation and high-dimensional optimisation problems in finance.
Jan Obloj develops numerical methods for martingale optimal transport problems which yield bounds for option prices and optimal transport techniques for model calibration.
Justin Sirignano has pioneered the use of Deep Learning methods for various applications in finance ranging from credit risk modeling to limit order book modeling.
Christoph Reisinger develops novel and efficient numerical methods for stochastic control problems and high-dimensional (S)PDEs and their applications in finance;
Terry Lyons devised cubature methods in Wiener space for solving stochastic differential equations.
Sam Howison and Jeff Dewynne were among the pioneers in the development of advanced  partial differential equation methods in finance, the use of asymptotic methods for their solution and their application to various markets such as energy and commodities.
Blanka Horvath develops numerical solutions for pricing, hedging and optimal investment problems and analytic- and asymptotic methods for a wide variety of stochastic models for equity, FX and interest rate modelling. The numerical methodologies explore path-dependent  data-driven machine learning solutions as well as quantum machine learning algorithms.

Behavioural finance

Hanqing Jin  develops quantitative models of investor behaviour, building on the fundamental work of Kahneman and Tversky's prospect theory and Lopes' SP/A theory. Ning Wang is working on sentiment analysis based on social media data, as well as on using data to establish metrics for learning and identification purposes.
Jan Obloj works on optimal decision problems for cumulative prospect theory agents and understanding their actions in dynamic environments, such as casino gambling.

For more information on research activities of our group please visit the individual websites of group members.