Thomas Barrau - Artificial Intelligence for Financial Markets: The Polymodel Approach

This series addresses the emerging advances in mathematical theory related to finance and application research from all the fintech perspectives. It is a series of monographs and contributed volumes focusing on the in-depth exploration of financial mathematics such as applied mathematics, statistics, optimization, and scientific computation, and fintech applications such as artificial intelligence, block chain, cloud computing, and big data. This series is featured by the comprehensive understanding and practical application of financial mathematics and fintech. This book series involves cutting-edge applications of financial mathematics and fintech in practical programs and companies.

The Financial Mathematics and Fintech book series promotes the exchange of emerging theory and technology of financial mathematics and fintech between academia and financial practitioner. It aims to provide a timely reflection of the state of art in mathematics and computer science facing to the application of finance. As a collection, this book series provides valuable resources to a wide audience in academia, the finance community, government employees related to finance and anyone else looking to expand their knowledge in financial mathematics and fintech.

The key words in this series include but are not limited to:

a) Financial mathematics

b) Fintech

c) Computer science

d) Artificial intelligence

e) Big data

This Springer imprint is published by the registered company Springer Nature Switzerland AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

This book exposes a manageable approach to exploit nonlinearity for the purpose of financial investment. It summarizes the research Raphael Douady and co-authors have conducted for nearly two decades now. This research is expanded on multiple aspects by a joint work conducted by Thomas Barrau.

In general, relationships between variables are nonlinear and noisy. When attempting to relate a target variable to several explanatory variables, modeling finely multi-dimensional linearity suffers from the curse of dimensionality without bringing blatant benefits. Polymodels simplify this approach by retaining unidimensional nonlinearities and proposing various aggregation methods according to the task at hand. For instance, in the case of prediction, each one-dimensional model produces a prediction. The most relevant ones are then selected, then possibly averaged in case of ambiguity, to yield the final prediction. In the case of defining a risk indicator, as downturns are usually associated with an increase of correlations, the distribution of goodness-of-fit metrics is analyzed. It can be seen as a form of ensemble learning.

The first task is to perform the one-dimensional nonlinear regressions. Several methods are presented, including non-parametric kernel regressions but the method of choice is linear regression on nonlinear functions (Hermite polynomials for their orthogonality properties) of the explanatory variable, further regularized by shrinkage to the linear component to mitigate overfitting.

Nonlinear transforms of initial factors can be used as new variables or features to feed a machine learning algorithm. Another use of extracted nonlinearities is to transform their convexity into an antifragility score (in the sense of N.N. Taleb). These scores can then be used as a factor to build long-short portfolios. The Polymodel approach can be implemented at the level of the market, industries, or individual stocks. With the help of Bayesian conditioning it can combine the information of hundreds of factors.

In summary, polymodels provide a very workable methodology to exploit nonlinearity for the purpose of investing, forecasting and risk management. Barrau and Douady describe the method and its application in this book filled with examples and backtests which will certainly inspire numerous finance practitioners.

Like many innovative ideas, polymodels emerged from a very stressful situation. Soon after we started the Riskdata venture, a new risk software aimed at the buy-side, the Twin Towers in New York were hit. This event would change the face of the world, and seriously put our nascent project at stake. There was no chance to sign a single contract for at least a year. While we were about to abandon the project and find a payroll job, a fund of hedge fund manager proposed the following challenge to us: given only audited monthly returns of the funds, what can we reliably say about their strategy, their risks, and how they fit in a portfolio, made of both liquid and alternative assets?

This challenge was way beyond the mere assessment of classical performance metrics, such as the Sharpe ratio, downside volatility, beta, FamaFrench factor analysis, etc. These measures, widely used by the industry, are known to provide relevant information from the past, but nothing truly reliable for the future behavior. We figured out that, if a software, however sophisticated, ignores the key points addressed in a conversation between an investor and a manager, it would miss the elephant in the room. So, we asked this manager to let us silently attend some of his meetings with the managers he was either invested in or planning to. To our surprise, the investor would spend only a few minutes talking about correlations and volatility, then the rest of the hour on specific moments that were relevant to the particular strategy: how did the manager weather such or such an event?; when and how did he flip his positions?; and other such questions. Our challenge was to put these questions into a software that was systematic enough to automatically address them. The idea was