DrPaul Bilokon

Paul Alexander Bilokon is Head of Market Making at MFT Energy.

He is also CEO and Founder of Thalesians Ltd, Chief Scientific Advisor (CSA) to Thalesians Marine Ltd, Head of Faculty at Machine Learning Institute (MLI), and Head of Faculty at Quantitative Developer Certificate (QDC).

He has served as a senior quantitative consultant at BNP Paribas, Citigroup, G-Research, qSpark, and other leading financial (and other) organizations, on the buy- and on the sell-side. He has also served as Head Quant in Markets Electronic Trading (MET) at Deutsche Bank, the global team that he had helped set up with Jason Batt and Martin Zinkin. Before Deutsche Bank, he worked at Morgan Stanley (in Andrew Hausler's and Nicholas Zinn's prime brokerage risk), Lehman Brothers (in Jim McCormick's, Anne Sanciaume's, and Alexei Jiltsov's FX research and Ronan Dowling's FX quants), Nomura (in FX e-trading, under Martin Zinkin, Abid Zaidi, and Mark Gardner), and Citigroup (first in FX quants under Sebastian del Bano Rollin, Nigel Khakoo, and Roger Vernon, then in electronic credit and rates trading), Paul pioneered electronic trading in credit with Rob Smith and William Osborn at Citigroup.

Paul Bilokon was voted Quant of the Year 2023 by Rebellion Research.

Paul has graduated from Christ Church, University of Oxford, with a distinction and Best Overall Performance prize. At Oxford he wrote a distinguished project, Bayesian methods for solving estimation and forecasting problems in the high-frequency trading environment, supervised by Daniel Jones. He also graduated twice from Imperial College London. His MSci thesis Visualising the Invisible: Detecting Objects in Quantum Noise Limited Images, supervised by Duncan Fyfe Gillies and Marin van Heel, won him the university's Donald Davis Prize and the British Computing Society SET Award for Student Making Best Use of IT.

Paul's lectures at Imperial College London in machine learning for MSc students in mathematics and finance and his course consistently achieves top rankings among the students.

Paul has made contributions to mathematical logic, domain theory, and stochastic filtering theory, and, with Abbas Edalat, has published a prestigious LICS paper. Paul has co-authored several books: Machine Learning and Big Data with kdb /q (with Jan Novotny, Aris Galiotos, and Frédéric Délèze, published by Wiley), and Machine Learning in Finance: From Theory to Practice (with Matthew F. Dixon and Igor Halperin, published by Springer). He is currently working on Python, Data Science, and Machine Learning (to be published by World Scientific).

Dr Bilokon is a Member of British Computer Society, Institution of Engineering and Technology, and European Complex Systems Society.

Paul is a frequent speaker at premier conferences such as Global Derivatives/QuantMinds, WBS QuanTech, AI, and Quantitative Finance conferences, alphascope, LICS, and Domains.

Teaching

MATH97112 - Computing in C++


The module gives an introduction to object-oriented programming in C++. In contrast to structured programming, where a programming task is simply split into smaller parts, which are then coded separately, the essence of object oriented programming is to decompose a problem into related subgroups, where each subgroup is self-contained and contains its own instructions as well as the data that relates to it. Starting from the simple concept of a class that contains both data and methods relating to that data, the module will cover all the major features of object-oriented programming, e.g. encapsulation, inheritance, and polymorphism. To this end, the module will address operator overloading, virtual functions, and templates.

MATH97119 - Advances in Machine Learning

The module introduces the latest advances in machine learning. We start with reinforcement learning and demonstrate how it can be combined with neural networks in deep reinforcement learning, which has achieved spectacular results in recent years, such as outplaying the human champion at Go. We also demonstrate how advanced neural networks and tree-based methods, such as decision trees and random forests, can be used for forecasting financial time series and generating alpha. We explain how these advances are related to Bayesian methods, such as particle filtering and Markov chain Monte Carlo. We apply these methods to set up a profitable algorithmic trading venture in cryptocurrencies using Python and kdb /q (a top technology for electronic trading) along the way.

Students

2014-2015 MSc in Computing (Software Engineering) Raymond Lee Approximating Algorithm for the Law of Brownian Motion (supervised jointly with Prof. Abbas Edalat)
2019-2020 MSc Mathematics and Finance William Howard Deep reinforcement learning in electronic market making
2019-2020 MSc Mathematics and Finance Chenyu Liu Deep reinforcement learning and electronic market making
2019-2020 MSc Mathematics and Finance Conor McIndoe A data driven approach to market regime classification
2019-2020 MSc Mathematics and Finance Toby Weston Distributional reinforcement learning for optimal execution
2019-2020 MSc Mathematics and Finance Xinyu (Cindy) Yan Forecasting cryptocurrency prices
2020-2021 MSc Mathematics and Finance Arvid Bertermann Reinforcement learning trading strategies with limit orders and high frequency signals
2020-2021 MSc Mathematics and Finance Kian Hatamieh European government bond volume prediction using dealer to client flow
2020-2021 MSc Mathematics and Finance Georgios Pampalis Price discovery of corporate bond composite using machine learning and Kalman filters
2020-2021 MSc Mathematics and Finance Viola Ruo Han Pu Pricing options using deep neural networks from a practical perspective: a comparative study of supervised and unsupervised learning
2020-2021 MSc Mathematics and Finance Tzyy Shyang Tong Reinforcement learning with continuous controls for foreign exchange trading
2020-2021 MSc Mathematics and Finance Hendrik Zimmermann Intraday trading with neural networks and deep reinforcement learning
2021-2022 MSc Mathematics and Finance Jan Jasper Eckstein Low latency finance
2021-2022 MSc Mathematics and Finance Baichu Guo Reinforcement learning in the electronic FX market making
2021-2022 MSc Mathematics and Finance Tom Ham Actor-critic reinforcement learning methods for electronic market making
2021-2022 MSc Mathematics and Finance Tianhao (Patrick) Wang Reinforcement learning provides free lunch, but at what cost?
2021-2022 MSc in Computing (Management and Finance) Yining (Frank) Kang Electronification and computerization of trading
2021-2022 MSc Advanced Computing Adithya (Adi) Sireesh Quantum machine learning
2021-2022 MSc Artificial Intelligence Quanlong Li Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Wei Jie Chua Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Cormac Conway Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Qi Huang Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Xuanjia Zhang Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Luming Zhang Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Yi Siang Ong Drug discovery with graph neural networks
2021-2022 MSc Artificial Intelligence Elizabeth Bates Drug discovery with graph neural networks
2021-2022 MSc Artificial Intelligence Yikang Li Drug discovery with graph neural networks
2021-2022 MSc Artificial Intelligence Qi Li Drug discovery with graph neural networks
2021-2022 MSc Artificial Intelligence Hongye Liu Drug discovery with graph neural networks
2021-2022 MSc Artificial Intelligence Abir Sridi Drug discovery with graph neural networks
2021-2022 MSc in Computing (Software Engineering) Bruno Wu Low-latency inter-process communication for high-frequency trading
2021-2022 MSc in Computing (Software Engineering) Ruo Chen Low-latency inter-process communication for high-frequency trading
2021-2022 MSc in Computing (Software Engineering) Dongchi Li Low-latency inter-process communication for high-frequency trading
2021-2022 MSc in Computing (Software Engineering) Wenzheng Shan Low-latency inter-process communication for high-frequency trading
2021-2022 MSc in Computing (Software Engineering) Zekun Yang Low-latency inter-process communication for high-frequency trading
2021-2022 MSc in Computing (Software Engineering) Weixuan Zeng Low-latency inter-process communication for high-frequency trading
2021-2022 MEng Computing Luqman Liaquat Capturing and visualizing cryptocurrency market data
2021-2022 MEng Computing Ayoob Ahmed Capturing and visualizing cryptocurrency market data
2021-2022 MEng Mathematics and Computer Science Sanchit Ajmera Capturing and visualizing cryptocurrency market data
2021-2022 BEng Computing Tyrell Duku Capturing and visualizing cryptocurrency market data
2021-2022 MEng Computing Mazen Hussein Capturing and visualizing cryptocurrency market data
2021-2022 MEng Computing Mustafa Ilyas Capturing and visualizing cryptocurrency market data
2021-2022 MEng Computing Abdur Sharif Capturing and visualizing cryptocurrency market data
2021-2022 MEng Computing Oliver Federico Benchmarking suite for high frequency C++ trading systems
2021-2022 BEng Mathematics and Computer Science Kamil Bujel Benchmarking suite for high frequency C++ trading systems
2021-2022 BEng Mathematics and Computer Science Dimitri Chamay Benchmarking suite for high frequency C++ trading systems
2021-2022 MEng Mathematics and Computer Science Peter Christofides Paton Benchmarking suite for high frequency C++ trading systems
2021-2022 MEng Computing (Artificial Intelligence and Machine Learning) Charles Dickie Benchmarking suite for high frequency C++ trading systems
2021-2022 MEng Computing Panagiotis Pachiyannis Benchmarking suite for high frequency C++ trading systems
2021-2022 MEng Mathematics and Computer Science Aris (Yi Qing) Zhu Benchmarking suite for high frequency C++ trading systems
2021-2022 MEng Computing (Artificial Intelligence and Machine Learning) Emily Haw Transformers versus LSTMs for electronic trading
2021-2022 BEng Computing Casey Williams Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU
2021-2022 BEng Mathematics and Computer Science Yash Yeola Deep learning models for UK electricity price forecasting
2021-2022 MEng Computing (Artificial Intelligence and Machine Learning) Sei Aoki Completing volatility surfaces with transformer-based variational autoencoders
2021-2022 BEng Computing Gordon Lee Programming strategies for low-latency applications
2021-2022 MEng Mathematics and Computer Science Yat Wong Simulating fractional Brownian motion and related stochastic processes
2021-2022 MEng Electronic and Information Engineering Edward Harriss Arbitrage strategies in cryptocurrency markets
2021-2022 MEng Mathematics and Computer Science James Pedley Combining deep learning on order books with reinforcement learning for profitable trading
2021-2022 MEng Electronic and Information Engineering Shafir Rahman Predicting cryptocurrency prices
2021-2022 MSc Computing Ronan Patrick Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Advanced Computing Adithya Sireesh Quantum machine learning
2021-2022 MSc Computing Alex Brady Cache-efficient C++ for high frequency trading
2021-2022 MSc Computing Daniel Pelnar Cryptocurrency spot-futures basis arbitrage
2021-2022 MSc Artificial Intelligence Abir Sridi Applying deep learning to calibrate stochastic volatility models
2021-2022 MSc Artificial Intelligence Sun Jin Kim Drug discovery with graph neural networks
2021-2022 MSc in Computing (Management and Finance) Aiden Deng Predicting cryptocurrency prices
2021-2022 MSc in Computing (Artificial Intelligence and Machine Learning) Boyu Han Classical statistics versus deep neural networks for cryptocurrency price prediction
2021-2022 MSc in Computing (Artificial Intelligence and Machine Learning) Nikita Lisitsyn Transformers for electronic trading
2021-2022 MSc Advanced Computing Ruijie Xiong Benchmarking specialized databases for high-frequency data
2021-2022 MSc in Computing (Management and Finance) Huixuan (Vanessa) Zhu GPUs for risk management
2021-2022 MSc in Computing (Management and Finance) Yitao Qiu Transformers versus LSTMs for electronic trading
2022-2023 MEng JMC Sanchit Ajmera Cryptocurrency spot-futures basis arbitrage
2022-2023 BEng Computing Alex Bainbridge Drug discovery with graph neural networks
2022-2023 BEng Computing Kavya Chopra Integral: integrating quantitative and computational frameworks
2022-2023 MEng Computing Ruxandra-Teodora Fleseriu C++ design patterns for low-latency applications including high-frequency trading
2022-2023 BEng JMC Zarya Mekathotti Machine learning for futures trading
2022-2023 BEng JMC Chi-Fei Nim Programming quantum computers
2022-2023 MEng Computing James Shipley Visual computing for electronic trading strategy development
2022-2023 BEng Computing Robert Stok Deep econometrics
2022-2023 MSc in Computing (Artificial Intelligence and Machine Learning) Pierre-Antoine Arsaguet Quasi-Monte Carlo methods for calculating derivatives sensitivities under stochastic volatility models on the GPU
2022-2023 MSc Advanced Computing Stelios Evagorou GPU computing
2022-2023 MSc Advanced Computing Hamad Mohammed Artificial consciousness
2022-2023 MSc Advanced Computing Paulius Sasnauskas Artificial consciousness
2022-2023 MSc in Computing (Software Engineering) Yaqi Zhou Simulating fractional Brownian motion and related stochastic processes
2022-2023 MEng Mathematics and Computer Science Wojtek Sowinski Template metaprogramming in modern C++
2022-2023 MEng Computing (Artificial Intelligence and Machine Learning) Daniel Mihalik Template metaprogramming in modern C++
2022-2023 MEng Computing Sean Ng Template metaprogramming in modern C++
2022-2023 BEng Mathematics and Computer Science Adrian Wong Template metaprogramming in modern C++
2022-2023 BEng Computing Felix Harman Template metaprogramming in modern C++
2022-2023 BEng Computing Kavya Chopra Template metaprogramming in modern C++
2022-2023 MEng Mathematics and Computer Science Aryaman Arora Template metaprogramming in modern C++
2022-2023 MSc Artificial Intelligence Tia Warner Drug discovery with graph neural networks
2022-2023 MSc Artificial Intelligence Victrix Gyasi Drug discovery with graph neural networks
2022-2023 MSc Artificial Intelligence Moez Mrad Drug discovery with graph neural networks
2022-2023 MSc Artificial Intelligence Anastasia Ilina Drug discovery with graph neural networks
2022-2023 MSc Artificial Intelligence Boyan Alipiev Drug discovery with graph neural networks
2022-2023 MSc Computing Jan Peter Image recognition based calorie tracker
2022-2023 MSc Computing Jason Lee Image recognition based calorie tracker
2022-2023 MSc Computing Pablo Behrens Image recognition based calorie tracker
2022-2023 MSc Computing Simon Frei Image recognition based calorie tracker
2022-2023 MSc Computing Ryan Perkins Image recognition based calorie tracker
2022-2023 MSc Computing Laxmi Prajapat Image recognition based calorie tracker
2022-2023 MSc Computing Yutong Chen Real-time margin calculations for cryptocurrency derivatives in kdb+/q
2022-2023 MSc Computing Burak Gunduz C++ design patterns for low-latency applications including high-frequency trading
2022-2023 MSc in Computing (Management and Finance) Chengtian He Combining deep learning on order books with reinforcement learning for profitable trading
2022-2023 MSc in Computing (Artificial Intelligence and Machine Learning) Koti Sreenivas Jaddu Combining deep learning on order books with reinforcement learning for profitable trading
2022-2023 MSc Computing Max Lucuta Semi-static conditions in low-latency C++ for high-frequency trading: better than branch prediction hints
2022-2023 MSc Mathematics and Finance Ilia Sobakinskikh Optimising Transformer neural network for real-time outlier detection on FPGAs
2022-2023 MSc Mathematics and Finance Yijun Dong Time series forecasting (working title)

Projects


Graph neural networks in finance
The field of drug discovery within life sciences is being revolutionized by the utilization of graph neural networks [WPCLZY].

In finance, the data are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. Graph neural networks are a natural candidate for such problems.

In this project we explore the potential of graph neural networks within finance.

[WPCLZY] Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, Philip S. Yu. A Comprehensive Survey of Graph Neural Networks. arXiv, 2019:

Deep Reinforcement Learning and Electronic Market Making
The often lucrative business of electronic market making [G] poses many mathematical challenges.

It can be viewed as a complex optimization problem, seeking to maximize returns, minimize risks, take advantage of a suite of "alpha" signals, while minimizing adverse selection and slippage.

It is natural to consider this problem through the prism of deep reinforcement learning methodology [BS, DHB].

Our goal is to utilize deep Q-learning [MKSGAWR] and variants thereof to learn the market making strategies for specific asset classes and trading venues.

[BS] Andrew Barto and Richard S. Sutton. Reinforcement Learning: An Introduction, second edition. MIT Press, 2018.

[DHB] Matthew F. Dixon, Igor Halperin, Paul Bilokon. Machine Learning in Finance: From Theory to Practice. Springer, 2020.

[G] Olivier Gueant. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making

[MKSGAWR] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, Martin Riedmiller. Playing Atari with Deep Reinforcement Learning. 2013.

Deep Reinforcement Learning in Order Execution
In [AC], Almgren and Chriss have proposed a theoretical framework for the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact.

Since then, Almgren himself has moved away from this framework, saying that market nuances are critical in optimal execution [D].

While it is difficult to incorporate these nuances into the original, stochastic dynamical control formulation of the problem, it is natural to consider it in through the prism of deep reinforcement learning methodology [BS, DHB].

Our goal is to utilise deep Q-learning [MKSGAWR] and variants thereof to learn the optimal order execution strategy for specific asset classes and trading venues.

[AC] Robert Almgren and Neil Chriss. Optimal Execution of Portfolio Transactions. 1999.

[BS] Andrew Barto and Richard S. Sutton. Reinforcement Learning: An Introduction, second edition. MIT Press, 2018.

[D] Sebastian Day. Why Robert Almgren no longer trades using Almgren-Chriss. Risk.net, 2017.

[DHB] Matthew F. Dixon, Igor Halperin, Paul Bilokon. Machine Learning in Finance: From Theory to Practice. Springer, 2020.

[MKSGAWR] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, Martin Riedmiller. Playing Atari with Deep Reinforcement Learning. 2013.

Econometrics, linear regression, ensemble methods and neural networks for financial time series forecasting
Classical econometrics [H], linear regression, ensemble methods, and neural networks [L, N] have all been employed for financial time series forecasting, known among the practitioners, particularly on the buy-side, as "alpha generation". As markets mature, alpha generation becomes more and more challenging.

While the theory of classical econometrics is academically the most developed, regression methods combined with careful feature selection and various "tricks of the trade" are favoured by practitioners.

While theoretically neural networks subsume the linear regression family of methods, in practice their calibration on financial time series is challenging.

The goal of this project is to compare the relative efficacy of these approaches and come up with a recommended set of algorithms for alpha generation.

[H] James D. Hamilton. Time Series Analysis. Princeton University Press, 1994.

[L] Francesca Lazzeri. Time Series Forecasting: An Applied Machine Learning Approach. O'Reilly, 2020.

[N] Aileen Nielsen. Practical Time Series Analysis: Prediction with Statistics & Machine Learning. O'Reilly, 2019.

Simulated Annealing (SA) versus Quantum Annealing (QA) versus Backpropagation for Neural Networks
The advent of deep neural networks has been to a large extent driven by the backpropagation algorithm [RHW], which relies on a gradient descent method (or modifications thereof) for finding weights in a feedforward network. Gradient descent and similar methods are bound by all of the problems of any hill climbing procedure, including the problem of local optima.

Simulated annealing (SA) has been introduced in [KGV] as a general method for solving optimization problems. The idea is to use thermal fluctuations to allow the system to escape from local optima of the cost function so that the system may reach the global optimum under the appropriate annealing schedule (the rate of decrease of temperature). If the temperature is decreased too quickly, the system may become trapped in a local optimum. Too slow annealing, on the other hand, is practically useless, although such a process should certainly bring the system to the global optimum.

Quantum annealing (QA) was introduced by [KN] and [FGSSD]. In QA, quantum tunneling effects cause transitions between states in the optimization problem, in contrast to the usual thermal transitions in SA.

The advent of quantum computers, including those optimized for solving QA problems, may eventually make it practicable to calibrate large/deep neural networks quickly and optimally, finding global, rather than local, optima in the search space.

Our goal is to develop efficient algorithms for calibrating neural networks on quantum computers using the QA ideas.

[RHW] David E. Rumelhart, Geoffrey E. Hinton, Ronald J. Williams. Learning representations by back-propagating errors. Nature, 1986.

[KGV] Scott Kirkpatrick, C.D. Gelatt, Mario P. Vecchi. Optimization by simulated annealing. Science, 1983.

[KN] Tadashi Kadowaki and Hidetoshi Nishimori. Quantum annealing in the transverse Ising model. Physical Review E, 1998.

[FGSSD] A.B. Finnila, M.A. Gomez, C. Sebenik, C. Stenson, J.D. Doll. Quantum annealing: A new method for minimizing multidimensional functions. Chemical Physics Letters, 1994.

Functional Reactive Programming for Real-Time Systems


Functional Reactive Programming (FRP) is a programming paradigm for reactive programming (asynchronous dataflow programming) using the building blocks of functional programming (e.g. map, reduce, filter). FRP has been used for programming graphical user interfaces (GUIs), robotics, games, and music, aiming to simplify these problems by explicitly modelling time.

Many financial applications, such as electronic trading platforms, are real-time systems.

Many open questions remain: for example, should the system be modelled explicitly as a directed acyclic graph (DAG)? How to minimize the impact of FRP overhead on the system's latency and so on.

The goal of this project is to come up with a reference open source implementation of a real-time financial system.

[E] Conal Elliott, Paul Hudak. Functional Reactive Animation. ICFP '97: http://conal.net/papers/icfp97/

[B] Stephen Blackheath, Anthony Jones. Functional Reactive Programming.

Low-latency Framework for High-Frequency Trading (HFT)
Very little [L, C, C1, A, S, R, G, S1] has been published in the literature on low-latency programming in C . Yet, this is a foundation of numerous high-frequency trading (HFT) businesses, such as Virtu Financial, Citadel Securities, Two Sigma Securities, Tower Research Capital, Jump Trading, DRW, Hudson River Trading, Quantlab Financial, XTX Markets, GTS. Tradebot Systems, Flow Traders, IMC Financial, Optiver, XR Trading [A].

The goal of this project is to come up with a reference open-source implementation of a high-frequency trading system.

[A] Evan Akutagawa. 15 Well-Known High Frequency Trading Firms. Medium, 2018: https://medium.com/automation-generation/15-well-known-high-frequency-trading-firms-f45292c56d05

[L] John Lockwood. A Low-Latency Library in FPGA Hardware for High-Frequency Trading. InsideHPC Report, 2012: https://www.youtube.com/watch?v=nXFcM1pGOIE

[C] Carl Cook. When a Microsecond Is an Eternity: High Performance Trading Systems in C . CppCon, 2017: https://www.youtube.com/watch?v=NH1Tta7purM

[C1] Carl Cook. Low Latency C for Fun and Profit. Pacific , 2017: https://www.youtube.com/watch?v=BxfT9fiUsZ4&t=167s

[A] Sam Adams. Low Latency Architecture at LMAX Exchange. QCon London, March, 2017: https://www.infoq.com/presentations/lmax-trading-architecture/

[S] Ariel Salihan. What I've Learned after Coding for HFT and Low Latency Systems. Medium, 29 November, 2018: https://medium.com/@ariel.silahian/what-ive-learned-after-coding-for-hft-and-low-latency-systems-b86d9ad07742

[R] Alexander Radchenko. Benchmarking C : From Video Games to Algorithmic Trading. Meeting C , 2018: https://www.youtube.com/watch?v=7YVMC5v4qCA

[G] Kevin A. Goldstein R. In-Memory Techniques: Low-Latency Trading. In-Memory Computing Summit, North America, 2018: https://www.youtube.com/watch?v=yBNpSqOOoRk

[S1] Nimrod Sapir. High Frequency Trading and Ultra Low Latency Development Techniques. Core C , 2019: https://www.youtube.com/watch?v=_0aU8S-hFQI