Non-linearity coefficient for a single risk factor
Where the stress scenario risk measure for which institutions are determining the non-linearity coefficient has been determined for a single risk factor, such non-linearity coefficient shall be determined as follows:
(a)
where the extreme scenario of future shock for the non-modellable risk factor does not coincide with either the downward calibrated shock or the upward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall set
for that non-modellable risk factor;
(b)
where the extreme scenario of future shock for the non-modellable risk factor coincides with the downward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall calculate the non-linearity coefficient in accordance with the following formula:
where:
—
;
—
;
—
ɸ is the estimate of the tail parameter for the non-modellable risk factor calculated in accordance with Article 19;
—
loss0 is the loss that occurs when the downward shock CSdown determined in accordance with Article 3(1), point (b) is applied to the non-modellable risk factor;
—
is the loss that occurs when a downward shock equal to is applied to the non-modellable risk factor, where CSdown is the downward shock determined in accordance with Article 3(1), point (b);
—
is the loss that occurs when a downward shock equal to is applied to the non-modellable risk factor, where CSdown is the downward shock determined in accordance with Article 3(1), point (b);
(c)
where the extreme scenario of future shock for the non-modellable risk factor coincides with the upward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall calculate the non-linearity coefficient in accordance with the following formula:
where:
—
;
—
—
ɸ is the estimate of the tail parameter for the non-modellable risk factor calculated in accordance with Article 19;
—
loss0 is the loss that occurs when the the upward shock CSup determined in accordance with Article 3(1), point (b) is applied to the non-modellable risk factor;
—
is the loss that occurs when an upward shock equal to is applied to the non-modellable risk factor, where CSup is the upward shock determined in accordance with Article 3(1), point (b);
—
is the loss that occurs when an upward shock equal to is applied to the non-modellable risk factor, where CSup is the upward shock determined in accordance with Article 3(1), point (b).
