Extreme price episodes such as bubbles and crashes are pervasive in cryptocurrency markets. While a growing body of literature has examined these phenomena in major cryptocurrencies, relatively few studies have investigated their presence and implications for stablecoins, whose prices are designed to maintain a relatively stable value compared to other cryptocurrencies. Moreover, the role of extreme events in volatility modeling and their spillover effects across digital assets remain relatively underexplored. To address this gap, this study employs the Bubble Crash-GARCH (BC-GARCH) model, which allows us to explicitly incorporate extreme price events into volatility modeling through the Phillips, Shi, and Yu (PSY) test. The detected bubble and crash episodes are included as dummy variables in the conditional mean equation of returns. The empirical analysis considers major cryptocurrencies such as Bitcoin and Ethereum together with the stablecoin Tether, and is conducted under several GARCH-type volatility specifications. Contagion effects are also investigated by incorporating Bitcoin bubble and crash signals into the volatility models of other digital assets. The BC-GARCH specification reduces the latent component of the data generating process and enhances volatility forecast accuracy relative to standard GARCH benchmarks. Moreover, extreme events in Bitcoin provide informative signals for the volatility dynamics of other cryptocurrencies.