Financial Risk Assessment Beyond VaR and CVaR with the Application of Topological Data Analysis

Abstract

This study aims to evaluate financial risk through the application of Topological Data Analysis (TDA), including methods such as constructing the Vietoris-Rips complex () and calculating Euclidean Distance to analyze the structure and assess the changes in stock price data under normal and abnormal market conditions. This leads to the development of a topological risk assessment measure called Topological VaR Distance (TVaRD), which complements traditional risk assessment measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR). The data used in this study consists of daily stock prices over the past five years, from January 1, 2019, to December 31, 2023, for five securities in the food and beverage sector: CPF.BK, CBG.BK, SAUCE.BK, ICHI.BK, and SAPPE.BK.

The study finds that Topological VaR Distance (TVaRD) can serve as a supplementary risk assessment measure to traditional methods at the 95% confidence level for stock price data. TVaRD provides additional information about risk and offers a more appropriate perspective on risk, potentially acting as an early warning system and complementing traditional risk assessments. For example, in the case of SAPPE.BK over the past five years, TVaRD significantly increased from 67.3759 to 404.2511, which aligns with a decrease in VaR from -9.61% to -11.84% and a decrease in CVaR from -12.11% to -36.74%. The decrease in VaR and CVaR indicates increased risk, and thus the increase in TVaRD similarly indicates heightened risk.