1. Under the historical method, institutions shall determine the downward calibrated shock from a time series of 10 business days returns for a non-modellable risk factor in accordance with the following formula:
\mathrm{downward\ calibrated\ shock} = \mathrm{ES}_{\mathrm{Left}}(\mathrm{Ret}) \times \left(0.95 + \frac{1}{\sqrt{N - 1.5}}\right)
where:
— | Ret denotes the time series of 10 business days returns of the non-modellable risk factor; |
— | \mathrm{ES}_{\mathrm{Left}} (\mathrm{Ret}) is the estimate of the left-tail expected shortfall for the time series Ret calculated in accordance with Article 11(1); |
— | N is the number of returns in the time series Ret. |
2. Institutions shall determine the upward calibrated shock from a time series of 10 business days returns for a non-modellable risk factor with the historical method in accordance with the following formula:
\mathrm{upward\ calibrated\ shock} = \mathrm{ES}_{\mathrm{Right}}(\mathrm{Ret}) \times \left( 0.95 + \frac{1}{\sqrt{N-1.5}} \right)
where:
— | Ret denotes the time series of 10 business days returns of the non-modellable risk factor; |
— | \mathrm{ES}_{\mathrm{Right}} (\mathrm{Ret}) is the estimate of the right-tail expected shortfall for the time series Ret calculated in accordance with Article 11(2); |
— | N is the number of returns in the time series Ret. |