Extreme Tail Risk in NOK Exchange Rates: A GARCH–Block-Maxima EVT Assessment

We study extreme tail risk in EUR/NOK, USD/NOK, and EUR/USD using an integrated GARCH–Block-Maxima EVT (GEV) framework. Layer A filters time-varying volatility via GARCH(1,1) to obtain standardized residuals; Layer B models monthly block maxima with a GEV distribution. To produce one-day VaR, we map daily confidence levels α to block-maxima probabilities α_B=α^B (with B=21 trading days) and rescale by next-day conditional volatility. Using daily data from 2015–2025, we find heavy tails across all pairs, with EUR/NOK exhibiting the heaviest tail (larger ξ ̂) and USD/NOK the largest extreme-scale. Back tests show reliable 99% VaR across pairs (coverage not rejected; no systematic clustering), while 95% reveals under-coverage for EUR/USD and mild clustering for USD/NOK—consistent with Block-Maxima’s emphasis on far tails. The framework is transparent and auditable; for moderate-tail control (95%), a light PoT overlay or t/skew-t innovations can improve calibration. Our results document economically meaningful cross-pair differences in NOK risk and provide a practical pipeline from filtered returns to daily far-tail capital metrics.