Value at Risk Models: Comparative Insights, Methodological Challenges, and Emerging Directions

Abstract

As financial markets grow increasingly volatile and interconnected, the accurate measurement of downside risk has become a cornerstone of sound institutional risk governance. Value-at-Risk remains one of the most widely applied metrics in financial risk management, providing institutions with a quantifiable framework for assessing potential portfolio losses across diverse market environments. Despite its prevalence, the comparative efficacy of four principal methodologies viz., Historical Simulation, Parametric, Monte Carlo, and Conditional Value at Risk models, continues to generate scholarly debate, with no comprehensive synthesis consolidating their relative merits. This review critically evaluates each methodology's theoretical foundations, practical implementations, strengths, and limitations across four analytical dimensions: estimation performance, sector-specific applicability, modelling advances, and underlying statistical principles. Findings confirm that no universally superior method exists; optimal model selection is contingent upon market structure, data availability, and institutional risk appetite. Historical Simulation falters under structural market breaks; Parametric model sacrifices accuracy for computational efficiency; Monte Carlo Simulation accommodates complex instruments at considerable computational cost; and Conditional model, though superior in capturing tail risk, introduces implementation complexity. Emerging hybrid frameworks and machine learning integrations increasingly offer pragmatic resolutions to these inherent trade-offs. This review furnishes researchers and practitioners with a structured, context-sensitive reference for informed Value at Risk methodology selection.