Beyond VaR and CVaR: Topological Risk Measures in Derivative Markets

Amit Kumar Jha

This paper introduces a novel approach to financial risk assessment by incorporating topological data analysis (TDA), specifically cohomology groups, into the evaluation of derivatives portfolios. The study aims to go beyond traditional risk measures like Value at Risk (VaR) and Conditional Value at Risk (CVaR), offering a more nuanced understanding of market complexities. Using both simulated and real-world data, we develop a new topological risk measure, termed Density Change Under Stress (DCUS). Preliminary results indicate a significant change in the density of the point cloud representing the financial time series during stress conditions, suggesting that DCUS may offer additional insights into portfolio risk and has the potential to complement existing risk management tools.