arch.univariate.var_ratio

arch.univariate.var_ratio(p: float | None = None, distribution: Distribution | None = None, parameters: Sequence[float] | ndarray[tuple[int], dtype[float64]] | Series | None = None) → float[source]

Ratio of Gaussian VaR to model-distribution VaR.

Parameters:
p: float | None = None

The probability of an exception that the VaR is designed for, which is the size of the tail, in the open interval (0, 0.5). It is 0.05 for a 95% VaR and 0.01 for a 99% VaR. The default is 0.001, a 99.9% VaR.

distribution: Distribution | None = None

Standardized distribution used to compute the model VaR. If not provided, uses the standard normal distribution.

parameters: Sequence[float] | ndarray[tuple[int], dtype[float64]] | Series | None = None

Distribution parameters. Must have one finite element for each parameter of distribution. Use None for parameterless distributions.

Returns:

Ratio of the Gaussian left-tail VaR to the VaR implied by the supplied model distribution.

Return type:

float

Raises:

  • TypeError – If p is not a real number, distribution is not a Distribution or parameters cannot be converted to numbers.

  • ValueError – If p is not in (0, 0.5), parameters does not have one finite element for each parameter of the distribution, or the model distribution does not produce a positive finite VaR.

Notes

VaR is named by its confidence level, and p is the probability of an exception, as in the VaR backtests such as kupiec_pof(). The ratio is \(\Phi^{-1}(p)/F^{-1}(p)\) where \(F\) is the standardized distribution.