The Limits of Conditional Volatility: Assessing Cryptocurrency VaR under EWMA and IGARCH Models

Abstract

The application of the standard static Geometric Brownian Motion (GBM) model for cryptocurrency risk management resulted in a systemic failure, evidenced by a 80.67% chance of loss in the 5% value-at-risk benchmark. This study addresses a critical literature gap by comparatively testing three conditional volatility models the EWMA/IGARCH baseline, an IGARCH model augmented with explicit mean reversion (IGARCH + MR), and a modified EGARCH-style asymmetric shock model within a correlated Monte Carlo VaR framework. Crucially, the analysis is applied specifically to high-beta altcoins (XRP, SOL, ADA), an asset class largely neglected by mainstream GARCH literature. Our results demonstrate that imposing stationarity (IGARCH + MR) drastically underestimates downside risk (5 percent value-at-risk reduced by 50%), while the asymmetric model (Model 3) leads to severe over-penalization. The EWMA/IGARCH baseline, characterized by infinite volatility persistence (alpha + beta = 1), provided the only robust conditional volatility estimate. This finding constitutes a formal rejection of the conventional financial hypotheses of volatility mean reversion and the asymmetric leverage effect in the altcoin asset class, establishing that non-stationary frameworks are a prerequisite for regulatory-grade risk modeling in this domain.