Analysing Indian Stock Market Crashes Through a Topological Lens

The Indian stock market is one of the world's largest and most dynamic financial markets. In the Indian equity market, indices serve as a means to assess the changes in the worth of representative clusters of stocks. This study analyses Indian stock market crashes through a topological lens. The daily log-returns of some Indian stock market indices: BSE SENSEX, BSE SMALLCAP, BSE 100, and BSE 500, were tracked. This investigation analysed the persistence landscapes and Lp-norms associated with these indices. The methodology employs topological data analysis, specifically in applying persistent homology to identify and measure topological patterns within the four-dimensional Indian stock indices time series data. To conduct the analysis, time-dependent point clouds were extracted using a sliding window technique, and these datasets were then associated with a topological space. The analysis aimed to identify transient loops and measure their persistence within this space. These findings were then encoded into mathematical functions known as persistence landscapes. The study also sought to assess the variations in these landscapes through their Lp-norms. The study observed that the Lp-norms rose in the run-up to major financial crises in the Indian stock market. Additionally, some statistical properties of these norms were studied.