On Estimating Bitcoin Value at Risk : A Comparative Analysis

We compare several models that forecast ex-ante Bitcoin one-day Value-at-Risk (VaR), starting from the simplest ones like Parametric Normal and Historical Simulation and arriving at Historical Filtered Bootstrap and Extreme Value Theory Historical Filtered Bootstrap. We also consider Gaussian and Student-t innovation in the GARCH model specification. The performance of all VaR models is validated using both statistical accuracy and efficiency evaluation tests. We evaluate model performances on four VaR confidence level (95%, 99%, 99.5% and 99.9%). We also validate the models under loss function backtests and our results confirm the efficacy of Historical Filtered Bootstrap as a methodology to estimate VaR. Furthermore, we find that the GARCH model with Gaussian innovation provides the best fit in term of estimating ex Ante VaR. In our empirical analysis, we find that, on the observed data (from November 8, 2012, to May 11, 2018), Historical Filtered Bootstrap AR-GARCH with Gaussian innovation correctly estimates VaR for all ε. The Parametric Normal and the standard Historical Simulation show their limitations and we suggest to avoid to use them. For backtest based on loss function, we find that for investors' viewpoint it seems better to choice Gaussian innovation in the GARCH specification, while under regulators' viewpoint suggest using Student-t innovation at least in the far tail