Statistical Methods in Finance 2024

Understanding Financial Markets: Some Explorations with Topological Data Analysis

By: Arnab Kumar Laha
Indian Institute of Management, Ahmedabad

The data emerging from the financial markets is complex allowing for the application of different tools to draw insights. Each tool brings with it unique capabilities to understand the market phenomenon. In this talk, I discuss the use of Topological Data Analysis (TDA) for financial market data. Beginning with a brief overview of TDA, we discuss some real-life applications in finance where the use of TDA yields interesting results. We examine the classification and clustering of time-series using TDA-based features which reveal interesting insights about some well-known stochastic processes. When the same is applied to time series of returns of Indian stocks we discover phenomena that are not identified by other data analytic techniques. In the context of pairs trading a strategy that is based on the use of TDA-based distance as a measure of dependence is found to be profitable than a competing Euclidean distance-based strategy. Some other applications of TDA-based techniques in financial markets are briefly reviewed.

This talk is broadly based on the following two papers:

1. Majumdar, S., and Laha, A. K. (2020). Clustering and classification of time series using topological data analysis with applications to finance. Expert Systems With Applications, 162, 113868. https://doi.org/10.1016/j.eswa.2020.113868
2. Majumdar, S., and Laha, A. K. (2023). Pairs trading with topological data analysis. International Journal of Theoretical and Applied Finance, 26(8), 2450002.