Downward and upward calibrated shock with the asymmetrical sigma method
Article 9
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; — 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 ; — 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 ; — ; (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; — 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 ; — 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 ; — .