Robust Tail Risk Estimation in Cryptocurrency Markets: Addressing GARCH Misspecification with Block Bootstrapping

This study examines the use of Filtered Historical Simulation (FHS) to estimate tail risk in cryptocurrency markets for the optimization of robustness in this area under model misspecification. An ARMA-GARCH model is employed on the daily returns on Binance Coin and Litecoin in order to compare the performance of classical and block bootstrap procedures in residual risk. Diagnostic tests indicate that standardized residuals are dependent, contrary to the independent and identically distributed (i.i.d.) assumption of conventional FHS. Comparing the block and ordinary bootstrapping approaches, we find that block bootstrap produces wider, more conservative confidence intervals, particularly in extreme tails (e.g., 0.1% and 99.9% percentiles). The findings suggest that block bootstrapping can be employed as a correction instrument in risk modeling where the standard volatility filters do not work. The article highlights the necessity to account for remaining dependencies and offers practical recommendations for more robust tail risk estimation during volatile markets.