Where the stress scenario risk measure for which institutions are determining the non-linearity coefficient has been determined for a non-modellable standardised bucket, the non-linearity coefficient shall be determined as follows:
where the extreme scenario of future shock does not correspond to a scenario identified in accordance with Article 6(1), point (b), where the value of the parameter β referred to in Article 6(1), point (c), it set equal to 1, institutions shall set the non-linearity coefficient
x = 1
for that non-modellable bucket;
where the extreme scenario of future shock is a scenario where the corresponding downward shock determined in accordance with Article 6(1), point (b) is applied to each risk factor in the non-modellable bucket, institutions shall calculate the non-linearity coefficient in accordance with the following formula:
\kappa = \min \left( \max \left[ \kappa_{\min}; 1 + \frac{\mathrm{loss}_{-1} - 2 \times \mathrm{loss}_{0} + \mathrm{loss}_{+1}}{2 \times \mathrm{loss}_{0}} \times (\mathrm{median} - 1) \times 25 \right]; \kappa_{\max} \right)
where:
x_{\min} = 0.9
;
x_{\max} = 5;
\mathrm{median}
is the median of the estimates of the tail parameters calculated in accordance with Article 19 for each of the risk factors within the bucket;
loss0 is the loss occurring when the corresponding downward shock determined in accordance with Article 6(1), point (b), is applied to each risk factor in the non-modellable bucket;
\mathrm{loss}_{1}
is the loss occurring when the corresponding downward shock determined in accordance with Article 6(1), point (b), multiplied by
\frac{4}{5}
is applied to each risk factor in the non-modellable bucket;
\mathrm{loss}_{+1}
is the loss occurring when the corresponding downward shock determined in accordance with Article 6(1), point (b), multiplied by
\frac{6}{5}
is applied to each risk factor in the non-modellable bucket;
where the extreme scenario of future shock is a scenario where the corresponding upward shock determined in accordance with Article 6(1), point (b), is applied to each risk factor in the non-modellable bucket, institutions shall calculate the non-linearity coefficient in accordance with the following formula:
\kappa = \min \left( \max \left[ \kappa_{\min}; 1 + \frac{\mathrm{loss}_{-1} - 2 \times \mathrm{loss}_{0} + \mathrm{loss}_{+1}}{2 \times \mathrm{loss}_{0}} \times (\mathrm{median} - 1) \times 25 \right]; \kappa_{\max} \right)
where:
x_{\min} = 0.9
;
x_{\max} = 5;
\mathrm{median}
is the median of the estimates of the tail parameters calculated in accordance with Article 19 for each of the risk factors within the bucket;
loss0 is the loss occurring when the corresponding upward shock determined in accordance with Article 6(1), point (b), is applied to each risk factor in the non-modellable bucket;
\mathrm{loss}_{1}
is the loss occurring when the corresponding upward shock determined in accordance with Article 6(1), point (b), multiplied by
\frac{4}{5}
is applied to each risk factor in the non-modellable bucket;
\mathrm{loss}_{+1}
is the loss occurring when the corresponding upward shock determined in accordance with Article 6(1), point (b), multiplied by
\frac{6}{5}
is applied to each risk factor in the non-modellable bucket.