1.   When assessing whether institution’s internal model is implemented with integrity as required by Article 325bi(1) of Regulation (EU) No 575/2013 in relation to the requirement for the expected shortfall risk measures referred to in Article 325bb of Regulation (EU) No 575/2013 to reflect historically observed data in accordance with Article 325bc(2), point (c), and Article 325bc(4), point (c), of that Regulation, competent authorities shall verify whether:

(a)	the distributional and any other relevant statistical assumptions used in the model, including volatility and correlations, are well justified, including with regard to the tail of the distributions relevant for the expected shortfall calculation;.

(b)

the empirical correlations that the institution uses when applying scenario of future shocks to reflect the joint movement of risk factors in the calculation of the expected shortfall risk measures referred to in Article 325bb of Regulation No 575/2013 are based on historically observed data in accordance with Article 325bc(2), point (c), and Article 325bc(4), point (c), of that Regulation.

For the purposes of point (b) of the first subparagraph, competent authorities may, where appropriate, require the institution to:

(a)	provide a sample of time series;

(b)	calculate the empirical correlations among those time series;

(c)	verify whether the correlations referred to in point (b) do not materially differ from the correlations used by the institution in its internal risk-measurement model.

2.   For the purposes paragraph 1, competent authorities shall compare, on the basis of a sample of time series:

(a)	the volatility and other distributional properties of the scenario of future shocks applied to a given risk factor in the calculation of the partial expected shortfall measures;

(b)	the volatility and other distributional properties of the returns observed for the given risk factor.

Competent authorities shall do the assessment referred to in paragraph 1 on the basis of both the period referred to in Article 325bc(4), point (c), of Regulation (EU) No 575/2013 and the period of financial stress referred to in Article 325bc(2), point (c), of that Regulation.

3.   For the purposes of paragraph 1, competent authorities may, on a sample of risk factors, perform additional tests, including normality tests, to assess whether the distributions assumed by the institution are adequate. Competent authorities may require the institution to provide the impact that using alternative distributions would have on the expected shortfall risk measures.