Portfolio VaR and Expected Shortfall by four methods (historical, parametric-normal, Cornish-Fisher, Monte Carlo) at confidence alpha.

asset_returns maps asset name -> equal-length list of daily returns; weights defaults to equal. Omit both to use the demo book. Divergence between historical and normal VaR is the fat-tail signal.

Fit GARCH(1,1) by maximum likelihood to a daily return series (>= 250 obs) and forecast volatility forecast_horizon days ahead (mean-reverting to long-run vol). Omit returns to use the demo portfolio.

Walk-forward VaR backtest (no look-ahead): Kupiec proportion-of-failures, Christoffersen independence/conditional-coverage tests, and the Basel traffic-light zone. method is 'historical' or 'parametric'. Needs more than window+30 observations; omit returns to use the demo portfolio.

Stress the portfolio two ways: a preset crisis-shock library (GFC-style equity crash, 2020 pandemic, +200bp rates, flight to quality, USD squeeze) and the portfolio's own worst horizon-day historical windows.

Extreme-value tail analysis: fit a Generalized Pareto to losses beyond the threshold_q quantile (peaks-over-threshold) and report EVT VaR/ES at alpha (use for 99.5%+ where empirical quantiles run out of data).

Score a retail loan application on a WoE logistic PD scorecard: 12-month probability of default, scorecard points (higher = safer) and a letter rating. Demo model trained on a synthetic book — methodology is production-style, the score is not a production score.

Metadata for the credit scorecard: held-out AUROC/Gini/KS, per-feature Information Values, and the valid categorical inputs.