In this research, I explore the factors driving extreme fluctuations in stablecoin prices concerning financial and cryptocurrency market indices. Through quantile models, I reveal the directional predictability of diverse financial variables, capturing extreme price variations and return distribution fluctuations. The outcomes highlight asymmetric pricing reactions and the impact of stablecoin stability mechanisms. The varying effects observed in stablecoin and cryptocurrency behavior imply a broader market link and potential fragility. Notably, intermediary constraints and stablecoin liquidity exhibit predictive power for subsequent price shifts in both tails, providing insights into the complex dynamics within cryptocurrency and stablecoin markets