Did Finance Oversleep a Century of Development in Physics?
Interview with NYU Machine Learning Professor Igor Halperin
Would you first briefly introduce yourself? How do you end up in quant while majoring in physics during your whole academic career?
I studied theoretical physics in St. Petersburg where I got my master's degree and started my PhD at the St. Petersburg Institute of Nuclear Physics. I completed my PhD at Tel-Aviv University after moving to Israel from Russia, and then did two postdocs in physics. As chances of landing a tenure track faculty position at that time were slim, I decided to move to the industry and find a field that would be both interesting, math-heavy, and in demand.
I have heard from my physics colleagues that finance was mostly about solving the diffusion equation under different boundary conditions, which did not sound too exciting to me. But around the same time some prominent physicists including J.P. Bouchaud, D. Sornette, E. Stanley and others turned to finance and established econophysics as a cross-disciplinary field that applies methods of physics to financial modeling, and reading these papers got me very interested in finance.
As a result, I learned about how to solve the Black-Scholes model using path integrals (a tool from physics) even before I learned how to solve it using more conventional tools used in finance. In a sense, I entered finance from a `back door’.
In the summer of 1999, I started my first job as a quantitative researcher at Bloomberg L.P. in a small R&D team made mostly of PhDs in math and physics.
2. Speaking of physics, do you think what you have learned helps you a lot during your career?
Yes, it helped in many ways, both generally as doing science gives you skills to do research, and also specifically, as the mathematical tools (such as differential equations, random processes etc.) What I learned in physics helped a lot to comprehend and master various financial models that share many mathematical techniques with physics.
Still, in hindsight, during most of my career as a quant it was far from obvious to me that given that I ended up in finance anyway, doing physics was the best way to prepare for it, as opposed e.g. to pursuing a PhD in computer science. However, my latest research that I pursued over the last two years, which initially focused on using inverse reinforcement learning for modeling financial markets, led me to some entirely unanticipated conclusions, and it was exactly my background in physics that helped me to find them.
My pretty dramatic conclusion was that financial academics collectively missed all the relevant development in physics starting from 1908 when Paul Langevin developed a generalization of the theory of Brownian motion of Einstein, which describes a Brownian particle moving in an external potential field. Einstein’s theory is mathematically equivalent to the Bachelier model from 1900 for stock prices. In its turn, the Bachelier model was reformulated as a model for a log-price (instead of the price itself) with a linear drift by Paul Samuelson in 1964, resulting in his celebrated Geometric Brownian Motion (GBM) model.
As the GBM model produces a poor fit to market data, financial engineers have since modified or extended it in myriad ways, proposing various stochastic volatility, jump-diffusion, Levy etc. models to ‘better match the market’.
I was quite shocked to find that a simple two-line comparison of two very famous equations, namely the GBM model and the Langevin equation, shows that the GBM model (as well as its multiple descends) describes a world with globally unstable dynamics, and thus does not make sense from the point of view of physics – at best, it can only be used to describe small market fluctuations over short period of time, but not dynamics that can proceed at arbitrary long times.
Though this observation is very basic, it appears that it has been overlooked since 1964 when the GBM model was proposed. I believe that if Samuelson was familiar with the Langevin equation from 1908, he would not propose his GBM model – just because the latter does not make sense!
Paraphrasing a famous quote about string theory, I would say that most financial models used by practitioners are ``not even wrong” - they are not about actual ‘physical’ markets, but rather about something else (a pure math).
Using ideas from both physics and reinforcement learning, Matthew Dixon and I proposed a new theoretically consistent model of market dynamics that we called ``Quantum Equilibrium-Disequilibrium” (QED). This research brings together finance, reinforcement learning and physics, and it is the direction I continue to pursue at the moment.
3. What are differences and similarities between doing purely academic research and working in the financial industry?
Research in the industry usually pursues objectives aligned with the needs of the business.
In industry, you are not after fundamental laws of nature, but rather looking for exploitable patterns to help the business you support. There is no requirement of scientific rigor, nor is it always that scientific methods of validation of results are enforced or controlled.
When scientific standards are severely compromised, it can result in bad practices. Landau used to say that about 80% of published research in peer-reviewed physics journals is either outright wrong or a useless tautology. If this is true for peer-reviewed physics journals, you can only imagine what the corresponding fraction for industrial or academic financial research might be.
4.What’s the biggest challenge you have ever met throughout your career development and how did you overcome?
My biggest challenge during my career as a quant was my distaste in C++, and a strong unwillingness to try to improve in it – all this during times when C++ was nearly a universal requirement for quants.
I overcame this challenge by proving that I can be useful without C++, by switching to Matlab and focusing on model prototyping and development, instead of supporting production quant libraries. I just sat out C++ until Python arrived, and then happily switched to it from Matlab.
5. How much do you think machine learning has brought to the financial industry?
Machine learning has tremendously enriched tools that are available to a researcher. In many cases, it has also brought some paradigm shifts, for example by focusing on data-driven methods.
6. Some people blame that algo trading accelerates the financial avalanche. What do you think?
I agree with them.
7. Both mutual funds like Fidelity and hedge funds are now applying ML during asset allocation. What are the different focuses of the two funds in using machine learning?
I think in general terms, the main difference is a time horizon, which is longer for mutual funds.
The methodology is similar, and can be stated in general terms in the language of reinforcement learning (RL), as we do in our upcoming textbook on Machine Learning in Finance (Springer 2020).
The reinforcement learning approach allows for a flexible choice of the objective of portfolio optimization, as well as the time horizon, signals used etc. So the math is very similar but the data used are different.
8. Do you think ML can predict the emergency like COVID-19 this time and avoid the drawback?
ML can definitely help with modeling pandemics. Modeling pandemics and propagation of infection diseases is a classical topic of statistical models. ML brings more flexibility to parametric models used in this field, and is therefore potentially capable of producing better forecasts.
On the other hand, there is a price – just because ML models are more flexible than classical stochastic models used for modeling pandemics, they have many more parameters to estimate, and hence need more data. To get better prepared for future pandemics, we need data from the current pandemic, plus the previous models, and then try to combine the two.
This would be a pragmatic way to move forward.
Alternatively, the same can be stated in terms of prior models or regularization, in the language of the machine learning community. When the amount of data is limited, we need strong priors – which is the same as good parametric models taken as priors.
9. (if yes) Will such high prediction accuracy make AI take the jobs of financial professionals?
I do not believe in the success of AI, not at least in its current form, without human supervision.
I am more of a believer in AI as a way to provide various helper tools to financial professionals rather than a way to replace them.
In finance, we just cannot proceed in the way of DeepMind’s MuZero and create an omnipotent AI super-trader.
Unlike classical games of Go or chess, markets are non-stationary and there is no fixed set of ‘rules of the game’ like in Go, so learning by self-play is not an option, or at least a very costly option.
Some people say they manage to train ML ‘deep everything’ models by creating realistic market simulators. But making a realistic market simulator is the same as building a good model of market dynamics, so I think this approach just replaces one hard problem by another. Strictly speaking, it is not even machine learning anymore – as machine learning is supposed to be data-driven.
10. Is there any hidden disadvantage or even danger of AI in the financial industry?
Definitely. AI is powerful and you should understand what you do when you use it.
Some people in finance tend to take a reasonable model, then misuse it badly, and then blame mathematicians for their failures. Just google ‘the formula that ruined Wall Street’ for one good example. So, I definitely see danger.
11. More specifically, I know you are mastered in reinforcement learning, What do you think the bottlenecks are for more widespread use of reinforcement learning in finance? Is it a lack of data, necessity for more computational power, or the need to develop further techniques?
There are no bottlenecks of any sort, except perhaps psychological, and this is exactly what I tried to argue with my research. Reinforcement learning is just the best way to think about option pricing, portfolio management, wealth management – in short, essentially about all of quantitative finance.
You can start with a very simple RL setting where the only thing you need is numerical linear algebra, and no neural networks are needed, but you can also go up in complexity by switching to different reward functions and relying on neural networks for function approximation.
12. How might inverse reinforcement learning be applied? Is the idea to create algorithms that learn directly from great investors?
IRL (Inverse Reinforcement Learning is defined as "the field of learning an agent's objectives, values, or rewards by observing its behavior.") may be applied in multiple ways. For example, one application is to use it for over-the-counter trading to infer preferences of trading counter parties. IRL could be used by banks to learn preferences of their corporate clients. Regulators can also rely on IRL methods to monitor stock exchanges.
13. How might reinforcement learning be applied outside of direct investments? Are there avenues in news analysis or portfolio optimization, areas where supervised learning techniques seem dominant?
I explained about RL in question 7).
14. Let’s come back to some chill questions. How’s your teaching experience in NYU?
It was my best time so far as a researcher. I wanted to create a course on machine learning in finance, and my initial plan was very different from what I ended up with. When teaching, you are forced to distill everything to the most basic and fundamental form.
When I tried to explain reinforcement learning, I thought that option pricing should be a great theoretical laboratory for this. This led to a paper on the QLBS model that detailed this idea, which in its turn led to next papers, etc. My views on how we should build better models have evolved quite a bit as a result.
What helped me a lot during this period was inspiration from one of my science heroes, Richard Feynman, who used to say that the best way to understand things is to try to explain them to a layman.
He was also encouraging us to look at things from another point of view. I think the example with the GBM model as a special case of the Langevin equation that I mentioned above can serve as an illustration to Feynman’s idea of another point of view. Take another point of view of the GBM model and all its descendants to see that they describe globally unstable worlds, and thus do not even make sense as self-consistent models!
15. You mention “That ability to quickly get a handle on the issue involved and come up with a solution will make you very valuable.” in the FRE. Could you give some advice on how to gain this ability?
When I was in college studying physics, I read the following advice from Arkady Migdal, an outstanding Soviet physicist, to young scientists. He said: “when you are faced with a new problem, first spend some time trying to solve it yourself without looking for how other people solved it. Most likely, you will not be able to solve it, but you will find the most important questions, so that your search at the next step would be more pointed.”
To give a simple example, let’s assume you tried linear regression with many predictors, and found your regression is quite unstable. Then you would search for a way to stabilize regression and would discover regularization. So, your learning process can be goal-oriented, rather than being abstract-linear, as is taught at school. There are both advantages and disadvantages in such goal-oriented learning. The advantage is the speed, the disadvantage is that you might miss something important when grabbing quasi-random pieces of wisdom here and there. The best way is to combine both given real-world time constraints.
16. Any advice for people who will step into this industry in the future
Yes, plan as far into the future as you can, and build your carrier accordingly. Consider continuous self-education. You will need to keep reinventing yourself. May I also suggest you take a look at our upcoming textbook?
About Professor Halperin:
Igor Halperin is a researcher at Fidelity Investment and a Research Professor of Financial Machine Learning at NYU Tandon School of Engineering. His research focuses on using methods of reinforcement learning, information theory, neuroscience and physics for financial problems such as portfolio optimization, dynamic risk management, and inference of sequential decision-making processes of financial agents. Igor has extensive industrial experience in statistical and financial modeling, in particular in the areas of option pricing, credit portfolio risk modeling, portfolio optimization, and operational risk modeling. Prior to joining Fidelity and NYU Tandon, Igor was an Executive Director of Quantitative Research at JPMorgan, and before that he worked as a quantitative researcher at Bloomberg LP. Igor has published numerous articles in finance and physics journals, and is a frequent speaker at financial conferences. He has also co-authored the books “Machine Learning in Finance: From Theory to Practice” (Springer 2020) and “Credit Risk Frontiers” (Bloomberg LP, 2012). Igor has a Ph.D. in theoretical high energy physics from Tel Aviv University, and a M.Sc. in nuclear physics from St. Petersburg State Technical University.
Written by Qian Pan & Edited by Michael Ding, Bryan Xiao & Alexander Fleiss