Risk analysis of China's stock markets based on topological data structures

ABSTRACT

We choose 100 stocks from China's markets and use their daily returns from January 3, 2013 to August 31, 2020 to investigate the risk situation in China's stock markets by exploring their correlations in the sample period. We build complexes and carry out topological data analysis on them. The persistence landscapes and their LP-norms show that there are three clear turbulent periods since 2013. The dates are then detected when the stocks are strongly correlated. As is well known, the financial risks easily break out and spread in such situations, so we call the dates critical dates for risks. We can also take them as the early warning signals for potential risks. We then construct planar maximal filtered graphs on the critical dates to help discover the systematically important companies. We find that they changed obviously in three different turbulent periods. It reminds us to analyze the risks' characteristics of the risks and implement risk prevention. The method combing topological data analysis and complex networks is shown to be effective in detecting critical information from markets, and hence is worth popularizing. © 2022 The Authors. Published by Elsevier B.V.