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:
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
x = 1
for that non-modellable risk factor;
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:
x = \min \left( \max \left[ x_{\min}; 1 + \frac{\mathrm{loss}_{-1} - 2 \times \mathrm{loss}_{0} + \mathrm{loss}_{+1}}{2 \times \mathrm{loss}_{0}} \times (-1) \times 25 \right]; x_{\max} \right)
where:
x_{\min} = 0.9
;
x_{\mathrm{\max}} = 5
;
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;
\mathrm{loss}_{1}
is the loss that occurs when a downward shock equal to
\frac{4}{5} \times \mathrm{CS}_{\mathrm{down}}
is applied to the non-modellable risk factor, where CSdown is the downward shock determined in accordance with Article 3(1), point (b);
\mathrm{loss}_{+1}
is the loss that occurs when a downward shock equal to
\frac{6}{5} \times \mathrm{CS}_{\mathrm{down}}
is applied to the non-modellable risk factor, where CSdown is the downward shock determined in accordance with Article 3(1), point (b);
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:
x = \min \left( \max \left[ x_{\min}; 1 + \frac{\mathrm{loss}_{-1} - 2 \times \mathrm{loss}_{0} + \mathrm{loss}_{+1}}{2 \times \mathrm{loss}_{0}} \times (-1) \times 25 \right]; x_{\max} \right)
where:
x_{\min} = 0.9
;
x_{\max} = 5;
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;
\mathrm{loss}_{1}
is the loss that occurs when an upward shock equal to
\frac{4}{5} \times \mathrm{CS}_{\mathrm{up}}
is applied to the non-modellable risk factor, where CSup is the upward shock determined in accordance with Article 3(1), point (b);
\mathrm{loss}_{+1}
is the loss that occurs when an upward shock equal to
\frac{6}{5} \times \mathrm{CS}_{\mathrm{up}}
is applied to the non-modellable risk factor, where CSup is the upward shock determined in accordance with Article 3(1), point (b).