Clustering Market Regimes Using the Wasserstein Distance

37 Pages Posted: 25 Oct 2021

See all articles by Blanka Horvath

Blanka Horvath

Mathematical Institute, University of Oxford and Oxford Man Institute; University of Oxford; The Alan Turing Institute

Zach Issa

King’s College London - Faculty of Natural and Mathematical Sciences

Aitor Muguruza

Imperial College London; Kaiju Capital Management

Date Written: October 22, 2021

Abstract

The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial time-series into a suitable number of temporal segments (market regimes).
As a special case of the above, we develop a robust algorithm that automates the process of classifying market regimes. The method is robust in the sense that it does not depend on modelling assumptions of the underlying time series as our experiments with real datasets show. This method -- dubbed the Wasserstein $k$-means algorithm -- frames such a problem as one on the space of probability measures with finite $p^\text{th}$ moment, in terms of the $p$-Wasserstein distance between (empirical) distributions. We compare our WK-means approach with a more traditional
clustering algorithms by studying the so-called maximum mean discrepancy scores between, and within clusters. In both cases it is shown that the WK-means algorithm vastly outperforms all considered competitor approaches. We demonstrate the performance of all approaches both in a controlled environment on synthetic data, and on real data.

Keywords: Stochastic processes, numerical methods, stochastic volatility models, regime classification, unsupervised learning

JEL Classification: C02, C14, C45, C82

Suggested Citation

Horvath, Blanka and Issa, Zacharia and Muguruza, Aitor, Clustering Market Regimes Using the Wasserstein Distance (October 22, 2021). Available at SSRN: https://ssrn.com/abstract=3947905 or http://dx.doi.org/10.2139/ssrn.3947905

Blanka Horvath

Mathematical Institute, University of Oxford and Oxford Man Institute ( email )

Andrew Wiles Building
Woodstock Road
Oxford, OX2 6GG
United Kingdom

University of Oxford ( email )

The Alan Turing Institute ( email )

Zacharia Issa (Contact Author)

King’s College London - Faculty of Natural and Mathematical Sciences ( email )

Strand
London, England WC2R 2LS
United Kingdom

HOME PAGE: http://https://www.kcl.ac.uk/people/zacharia-issa

Aitor Muguruza

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Kaiju Capital Management ( email )

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