quantlab.model.evaluation.volatility_level_metrics

quantlab.model.evaluation.volatility_level_metrics(pred, target)

Return the level metrics of a volatility prediction, qlike and variance_ratio.

Both compare predicted and realised variance on the cells where the prediction and the target are finite and positive (a non-positive volatility has no variance ratio). qlike is the mean over those cells of q - log(q) - 1 with q = target**2 / pred**2: zero for a perfect prediction, and it penalises an under-prediction of variance more than an over-prediction of the same size; a prediction close to zero where the target is not makes it very large, and infinite (written as null in a run’s run.json) once q overflows, which flags a model predicting next to no risk. variance_ratio is mean(target**2) / mean(pred**2), pooled over cells, so the most volatile symbols weigh most: 1 when the predicted variance is unbiased, above 1 when risk is under-predicted.

Parameters:

predarray_like

A 2-D [T, S] panel of predicted volatilities.

targetarray_like

A 2-D [T, S] panel of realised volatilities, on the same scale.

Returns:

dict[str, float]

{"qlike": ..., "variance_ratio": ...}, NaN without a usable cell.

Examples

A prediction of half the realised volatility on every cell, so a quarter of its variance:

>>> volatility_level_metrics([[0.1, 0.2]], [[0.2, 0.4]])
{'qlike': 1.6137056388801092, 'variance_ratio': 4.0}