Chapter 4, Article 19 · Commission Delegated Regulation (EU) 2024/397

Contents

Article 19Calculation of the estimate of the tail parameter#

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:ɸ1αNαNi1Reti2αN – αNRetαN12EŜLeftRet2where:

—α2,5 %;

—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;

—Reti represents the i-th smallest return in the time series Ret;

—αN denotes the integer part of αN;

—EŜLeftRet 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:ɸ1αNαNi1 – Reti2αN – αN – RetαN12EŜRightRet2where:

—α2,5 %;

—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;

—– Reti represents the i-th smallest return in the time series – Ret;

—αN denotes the integer part of αN;

—EŜRightRet 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 ɸ1,04.