GARCH Models and Alternative Distributions in Risk Forecasting: Application to Amazon Data

Keyuan Cao

doi:10.54097/hc4hsj36

Authors

Keyuan Cao

DOI:

https://doi.org/10.54097/hc4hsj36

Keywords:

GARCH-family models, Distributional assumptions, Value at Risk (VaR), Expected Shortfall (ES), Volatility Modeling

Abstract

Accurate estimate of tail risk remains a major difficulty in quantitative finance. Standard volatility models provide practical frameworks, but their success is dependent on both model dynamics and the distributional specification applied to the innovations. This study analyzes the statistical performance of four general GARCH-family models (sGARCH, eGARCH, GJR-GARCH, and apARCH) under three distributional assumptions (Gaussian, Student’s t, and skewed Student’s t). The objective is to evaluate how it combined effects of structural design and distributional choice on the reliability of Value-at-Risk (VaR) and Expected Shortfall (ES) predictions. Risk projections are calculated at 95% and 99% confidence levels using adjusted closing prices of Amazon.com, Inc. (AMZN) and are checked by Kupiec’s Proportion of Failures test (POF), Christoffersen’s Independence test, and the Conditional Coverage test (CC). The empirical evidence shows that heavy-tailed models provide more conservative and statistically reliable estimates of tail risk, while Expected Shortfall (ES) indicates more resilience compared to Value at Risk (VaR) under volatile conditions. The results demonstrate the relationship between volatility model design and innovation distribution, contributing to the literature on statistical risk modeling and offering methodological guidance for the application of GARCH-type processes in financial econometrics and machine learning.

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