Updated 23/11/2024
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CRR ToolDelegated Regulation 2024/397
Article 9

Article 9 - Downward and upward calibrated shock with the asymmetrical sigma method

Article 9

Downward and upward calibrated shock with the asymmetrical sigma method

Under the asymmetrical sigma method, institutions shall determine the downward and upward calibrated shock from a time series of 10 business days returns for a non-modellable risk factor by applying the following steps in the following order:

(a)

they shall determine the median of the returns within the time series, and split the 10 business days returns comprised in that time series into the following two subsets:

(i)

the subset of 10 business days returns the value of which is equal to or lower than the median;

(ii)

the subset of 10 business days returns the value of which is greater than the median;

(b)

for each subset referred in point (a), they shall compute the mean of the 10 business days returns in the subset;

(c)

they shall determine the downward calibrated shock in accordance with the following formula:

downward calibrated shock

Formula

where:

—

Ret denotes the time series of 10 business days returns of the non-modellable risk factor;

—

Ret i is the i-th return in the 10 business days returns time series Ret;

—

m is the median of the 10 business days returns time series Ret;

—

Formula
denotes the mean of the 10 business days returns computed in accordance with point (b) on the subset identified in accordance with point (a)(i);

—

N down is the number of 10 business days returns in the subset determined in accordance with point (a)(i);

—

N is the number of returns in the 10 business days returns time series Ret;

—

Formula
;

(d)

they shall determine the upward calibrated shock in accordance with the following formula:

upward calibrated shock

Formula

where:

—

Ret denotes the time series of 10 business days returns of the non-modellable risk factor;

—

Ret i is the i-th return in the 10 business days returns time series Ret;

—

m is the median of the 10 business days returns time series Ret;

—

Formula
denotes the mean of the 10 business days returns computed in accordance with point (b) on the subset determined in accordance with point (a)(ii);

—

N up is the number of returns in the subset determined in accordance with point (a)(ii);

—

N is the number of returns in the 10 business days returns time series Ret;

—

Formula
.