Identifying extreme events in the stock market: A topological data analysis.

This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices separately, could not detect EEs for multiple time series in one go. TDA provides a robust framework for such analysis and identifies the EEs during the crashes for different indices. The TDA analysis shows that L1, L2 norms and Wasserstein distance (WD) of the world leading indices rise abruptly during the crashes, surpassing a threshold of μ+4∗σ, where μ and σ are the mean and the standard deviation of norm or WD, respectively. Our study identified the stock index crashes of the 2008 financial crisis and the COVID-19 pandemic across continents as EEs. Given that different sectors in an index behave differently, a sector-wise analysis was conducted during the COVID-19 pandemic for the Indian stock market. The sector-wise results show that after the occurrence of EE, we have observed strong crashes surpassing μ+2∗σ for an extended period for the banking, automobile, IT, realty, energy, and metal sectors. While for the pharmaceutical and FMCG sectors, no significant spikes were noted. Hence, TDA also proves successful in identifying the duration of shocks after the occurrence of EEs. This also indicates that the banking sector continued to face stress and remained volatile even after the crash. This study gives us the applicability of TDA as a powerful analytical tool to study EEs in various fields.