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.

翻译：将标准的静态几何布朗运动模型应用于加密货币风险管理导致了系统性失效，其证据为在5%风险价值基准下出现损失的概率高达80.67%。本研究通过比较测试三种条件波动率模型——EWMA/IGARCH基准模型、加入显式均值回归的IGARCH模型以及改进的EGARCH式非对称冲击模型，并将其置于相关的蒙特卡罗风险价值框架中，从而填补了文献中的一个关键空白。尤为重要的是，该分析专门应用于高贝塔值的竞争币，此类资产在主流GARCH文献中很大程度上被忽视。我们的结果表明，强制施加平稳性会严重低估下行风险，而采用非对称模型则会导致过度惩罚。以无限波动持续性为特征的EWMA/IGARCH基准模型提供了唯一稳健的条件波动率估计。这一发现正式否定了关于竞争币资产类别中波动率均值回归和非对称杠杆效应的传统金融假设，并确立了非平稳框架是该领域达到监管级风险建模要求的先决条件。