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
where:
—
Ret denotes the time series of 10 business days returns of the non-modellable risk factor;
—
Reti 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;
—
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);
—
Ndown 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;
—
;
(d)
they shall determine the upward calibrated shock in accordance with the following formula:
upward calibrated shock
where:
—
Ret denotes the time series of 10 business days returns of the non-modellable risk factor;
—
Reti 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;
—
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);
—
Nup 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;
