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:
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:
the subset of 10 business days returns the value of which is equal to or lower than the median;
the subset of 10 business days returns the value of which is greater than the median;
for each subset referred in point (a), they shall compute the mean of the 10 business days returns in the subset;
they shall determine the downward calibrated shock in accordance with the following formula:
downward calibrated shock
\left(-\mu_{\mathrm{Ret} \le m} + \mathrm{C}_{\mathrm{ES}} \times \sqrt{\frac{1}{\mathrm{N}_{\mathrm{down}} - 1, 5} \times \sum_{i=1, \mathrm{\mathrm{Ret}}_i \le m}^{\mathrm{N}} \left(\mathrm{Ret}_i - \mu_{\mathrm{Ret} \le m}\right)^2}\right) \times \left(0, 95 + \frac{1}{\sqrt{\mathrm{N}_{\mathrm{down}} - 1, 5}}\right)
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;
\mu_{\mathrm{Ret}\le m}
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;
C_{\mathrm{ES}} = 3
;
they shall determine the upward calibrated shock in accordance with the following formula:
upward calibrated shock
\left(\mu_{\mathrm{Ret}>\mathrm{m}} + \mathrm{C}_{\mathrm{ES}} \times \sqrt{\frac{1}{\mathrm{N}_{\mathrm{up}} - 1.5} \times \sum_{\mathrm{i}=1, \mathrm{Ret}_{\mathrm{i}}>\mathrm{m}}^{\mathrm{N}} (\mathrm{Ret}_{\mathrm{i}} - \mu_{\mathrm{Ret}>\mathrm{m}})^2}\right) \times \left(0.95 + \frac{1}{\sqrt{\mathrm{N}_{\mathrm{up}} - 1.5}}\right)
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;
\mu_{\mathrm{Ret}>m}
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;
C_{\mathrm{ES}} = 3
.