Abstract
This study aims to deepen the understanding of the Rare Disaster Concern Index (RIX) by redefining its concept, developing its exact model within the Gram–Charlier density, and constructing its time series to enhance its theoretical foundation and numerical application in capturing extreme market risks. Through comparative analysis with conventional indices across various term structures, we uncover the capability of the RIX in reflecting higher-order risks in financial markets. Our findings demonstrate the heightened sensitivity of the RIX to extreme market movements, especially within the left lower range, emphasizing its importance in strategic risk management and investment decision-making.