Some applications of TDA on financial markets

The Topological Data Analysis (TDA) has had many applications. However, financial markets has been studied slightly through TDA. Here we present a quick review of some recent applications of TDA on financial markets and propose a new turbulence index based on persistent homology -- the fundamental t...

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Bibliographic Details
Published inIDEAS Working Paper Series from RePEc
Main Authors Ruiz-Ortiz, Miguel Angel, Jos'e Carlos G'omez-Larra~naga, Rodr'iguez-Viorato, Jes'us
Format Paper
LanguageEnglish
Published St. Louis Federal Reserve Bank of St. Louis 01.01.2022
Subjects
COVID-19
Securities markets
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Summary:The Topological Data Analysis (TDA) has had many applications. However, financial markets has been studied slightly through TDA. Here we present a quick review of some recent applications of TDA on financial markets and propose a new turbulence index based on persistent homology -- the fundamental tool for TDA -- that seems to capture critical transitions on financial data, based on our experiment with SP500 data before 2020 stock market crash in February 20, 2020, due to the COVID-19 pandemic. We review applications in the early detection of turbulence periods in financial markets and how TDA can help to get new insights while investing and obtain superior risk-adjusted returns compared with investing strategies using classical turbulence indices as VIX and the Chow's index based on the \\textit{Mahalanobis} distance. Furthermore, we include an introduction to persistent homology so the reader could be able to understand this paper without knowing TDA.