Modelling and Forecasting  Financial Volatility : An Application of GARCH Models in Risk Management

This project examines the modeling and forecasting of financial volatility using a comprehensive suite of GARCH family models, including standard GARCH, IGARCH, GJR-GARCH, and EGARCH, each estimated across various orders. Utilizing daily return data from the Euro Stoxx 50 index from 2015 to 2025, the study evaluates model performance using statistical criteria such as AIC, BIC, and log-likelihood, alongside out-of-sample forecasting accuracy. The empirical analysis reveals that the EGARCH(1,1) model delivers superior performance, effectively capturing asymmetry, volatility clustering, and fat-tailed distributions in financial returns. Volatility forecasts generated from the EGARCH(1,1)modeldemonstrate strong alignment with observed market behavior and provide more accurate Value-at-Risk (VaR) estimates. These results highlight the practical relevance of advanced GARCH-type models in financial risk management, particularly in dynamic and turbulent market conditions.