Revisiting Risk Measurement: Probability Distributions and Their Role in Financial Risk Management

Abstract

Effective risk measurement lies at the core of modern financial decision-making, regulatory compliance, and portfolio management. This paper investigates the conceptual and theoretical dimensions of probability distributions in financial risk assessment. Traditional reliance on the normal distribution has proven insufficient, especially under extreme market conditions where fat tails, skewness, and volatility clustering prevail. Drawing on an extensive review of pre-2009 international literature, this study evaluates the limitations of the Gaussian model and explores alternative approaches such as the Generalized Pareto Distribution, Student’s t-distribution, and Extreme Value Theory. The research employs a qualitative, document-based methodology to synthesize key theoretical contributions and assess their relevance in contemporary risk management. Findings demonstrate that model selection critically influences key risk metrics like Value-at-Risk (VaR) and Conditional VaR (CVaR). Integrating alternative distributions enhances predictive accuracy and provides a more robust framework for managing rare, high-impact financial events. This paper contributes to both academic theory and practical applications by offering pathways for integrating empirically grounded models into financial institutions’ risk architecture. These insights are vital for improving the resilience of risk management frameworks and informing policy under conditions of uncertainty and systemic vulnerability.