The impact of aggregator composition on liquidity provision in over-the-counter markets

The purpose of this project is to study the interaction between a trader and a given number of liquidity providers in an over-the-counter market. An example of an over-the-counter market is the FX market, which is the largest financial market in the world with a daily volume of several trillion dollars. Unlike the stock market, which is organised into exchanges with transparent limit order books, the FX market hinges on bi-lateral trading with liquidity providers. This is typically done in an aggregator, a technology that consolidates liquidity from several sources in the form of a limit order book.

This research aims to address a void in the literature regarding issues specific to liquidity provision in a`blind auction' over-the-counter setting. This topic has received limited attention up to this point, in stark contrast with optimal market making and optimal execution problems in stock markets. This is mostly due to the differences in the information structures between these two types of markets. In a `blind auction 'over-the counter setting, a liquidity provider is unaware of the prices offered to a trader by other liquidity providers. In a stock market, however, market participants are typically aware of the exact shape of the limit order book. This data is also easily accessible, unlike the confidential prices offered by liquidity providers in an over-the-counter market.

Due to the asymmetric information structure in over-the counter markets, it is challenging to find tractable models that are consistent with the microstructure. This research contributes to the literature by providing theoretical results in the setting when information is shared across the liquidity providers. While this is a strong assumption, the results provide a useful benchmark for experiments that are consistent with the microstructure. Such experiments involve liquidity providers having to compromise exploration and exploitation in an uncertain environment (for example, running multi-armed bandit algorithms). They shed light on practical aspects of over-the-counter market making such as algorithmic collusion.

All in all, this research should improve the quality of liquidity provision in over-the-counter markets by illustrating how certain trader behaviours can lead to situations that are unfavorable for both the traders and the liquidity providers. For example, a trader may attempt to interact with as many liquidity providers as possible, but in fact one can argue about an optimal number of liquidity providers in an aggregator. A trader can also create a prisoner's dilemma setting by mixing liquidity providers with different risk management styles. While these problems are well known among liquidity providers, there is value in having rigorous mathematics as well as extensive simulations to support the messages conveyed to traders.

This project falls within the EPSRC Statistics and applied probability research area. It is done in collaboration with the Fixed Income and Currencies Quantitative Trading department at Deutsche Bank AG.

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