This thesis analyzes the volatility behavior of two cryptocurrencies, Bitcoin (BTC) and Ethereum Classic (ETC), across three phases surrounding the COVID-19 pandemic: pre-pandemic, duringpandemic, and post-pandemic. We assess differences in return volatility and downside risk using GARCH (1,1) models and a modified Value-at-Risk (VaR) approach based on the CornishFisher expansion. We find that BTC, as a large-cap asset, displays more structured volatility patterns and stabilizes more quickly, whereas ETC, a small-cap coin, exhibits more erratic and sentiment-driven volatility. These differences are most pronounced during crisis conditions, where BTC may act as a volatility transmitter and ETC as a volatility amplifier. The findings support the hypothesis that market capitalization plays a key role in determining both persistence and systemic transmission of volatility. Offering practical insights for investors, risk managers, and policymakers navigating crypto-related risks.