Statistical Methods for Measuring Financial Market Risk: A Literature Review

Financial market risk arises from adverse changes in asset values and is commonly assessed through volatility, Value at Risk (VaR), and tail risk. This literature review compares the variance–covariance method, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, historical simulation, and Extreme Value Theory (EVT). Quantile regression is considered as a supplementary approach to dynamic VaR estimation. The methods are evaluated according to their statistical assumptions, predictive accuracy, tail-risk identification, data requirements, computational complexity, and practical suitability. The literature indicates that the variance–covariance method is efficient but vulnerable to distributional and linearity assumptions. GARCH models respond to time-varying volatility, although their performance depends on model specification and the innovation distribution. Historical simulation is transparent and accommodates portfolio revaluation, but relies on the relevance of past observations. EVT provides a direct framework for extreme losses but is sensitive to threshold selection and limited tail data. Backtesting remains necessary because theoretical flexibility does not ensure accurate forecasts. No method consistently dominates across all market conditions. Reliable measurement requires model selection to reflect return characteristics, portfolio structure, forecast purpose, and data availability. In some applications, combined methods provide a more appropriate representation of volatility dynamics and tail severity.