Randomized geometric tools for anomaly detection in stock markets

Cyril Bachelard (), Apostolos Chalkis (), Vissarion Fisikopoulos and Elias Tsigaridas ()
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Cyril Bachelard: UNIL - Université de Lausanne = University of Lausanne
Apostolos Chalkis: GeomScale Org.
Vissarion Fisikopoulos: NKUA - National and Kapodistrian University of Athens, GeomScale Org.
Elias Tsigaridas: OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs - IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité - Centre Inria de Sorbonne Université - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, GeomScale Org.

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Abstract: We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of geodesically non-convex and non-connected spherical patches that arise by intersecting a non-standard simplex with a sphere. To sample, we introduce two novel Markov Chain Monte Carlo (MCMC) algorithms that exploit the geometry of the problem and employ state-of-the-art continuous geometric random walks (such as Billiard walk and Hit-and-Run) adapted on spherical patches. To our knowledge, this is the first geometric formulation and MCMC-based analysis of the volatility puzzle in stock markets. We have implemented our algorithms in C++ (along with an R interface) and we illustrate the power of our approach by performing extensive experiments on real data. Our analyses provide accurate detection and new insights into the distribution of portfolios' performance characteristics. Moreover, we use our tools to show that classical methods for low-volatility anomaly detection in finance form bad proxies that could lead to misleading or inaccurate results.

Date: 2023-04-25
New Economics Papers: this item is included in nep-cmp
Note: View the original document on HAL open archive server: https://hal.science/hal-04223511v1
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Published in 26th International Conference on Artificial Intelligence and Statistics (AISTATS), Apr 2023, Valencia, Spain

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04223511

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