Calculation of the estimate of the tail parameter
Article 19
Institutions shall calculate the estimate of the tail parameter for a given non-modellable risk factor as follows: (a) where institutions used the historical method set out in Article 8 for determining the downward and upward calibrated shock of that non-modellable risk factor and the extreme scenario of future shock is the downward calibrated shock, they shall calculate the estimate of the tail parameter in accordance with the following formula: where: — ; — Ret is the time series of 10 business days returns for the non-modellable risk factor used in the historical method set out in Article 8; — represents the i-th smallest return in the time series Ret ; — denotes the integer part of ; — is the estimate of the left-tail expected shortfall for the time series Ret calculated in accordance with Article 11(1); (b) where institutions used the historical method set out in Article 8 for determining the downward and upward calibrated shock of that non-modellable risk factor and the extreme scenario of future shock is the upward calibrated shock, they shall calculate the estimate of the tail parameter in accordance with the following formula: where: — ; — Ret is the time series of 10 business days returns for the non-modellable risk factor used in the historical method set out in Article 8; — represents the i-th smallest return in the time series ; — denotes the integer part of ; — is the estimate of the right-tail expected shortfall for the time series Ret calculated in accordance with Article 11(2); (c) in all other cases institutions shall set the estimate of the tail parameter .