General requirements
1. For the purposes of Article 325bg(2) of Regulation (EU) No 575/2013, institutions shall calculate, for a given trading desk’s portfolio, the Spearman correlation coefficient laid down in Article 7 of this Regulation, and the Kolmogorov-Smirnov test metric laid down in Article 8 of this Regulation and, based on the results of those calculations, apply the criteria referred to in Article 9 of this Regulation. Where, according to those criteria, the theoretical changes and the hypothetical changes in the value of a trading desk portfolio are not sufficiently close, institutions shall be subject to the consequence set out in Article 10 of this Regulation.
2. For the purposes of paragraph 1, institutions may align the point in time (snapshot time) for which they calculate the theoretical changes in the trading desk portfolio’s value with the snapshot time for which they calculate the hypothetical changes in that value.
Calculation of the Spearman correlation coefficient
1. Institutions shall calculate the Spearman correlation coefficient referred to in Article 6(1) of this Regulation by performing the following steps in the following order:
(a)
they shall determine the time series of observations of the hypothetical and theoretical changes in the trading desk portfolio’s value for the most recent 250 business days;
(b)
from the time series of the hypothetical and theoretical changes referred to in point (a), institutions shall produce the corresponding time series of ranks in accordance with paragraph 2, treating the time series of the hypothetical and theoretical changes as the originating time series;
(c)
they shall calculate the Spearman correlation coefficient in accordance with the following formula:
Where:
R
HPL
=
the time series of ranks produced from the time series of hypothetical changes referred to in point (b);
R
RTPL
=
the time series of ranks produced from the time series of theoretical changes referred to in point (b);
=
the standard deviation of the time series of ranks R HPL
calculated in accordance with paragraph 3, point (a);
=
the standard deviation of the time series of ranks R RTPL
calculated in accordance with paragraph 3, point (b);
cov ( R HPL
, R RTPL
)
=
the covariance calculated in accordance with paragraph 3, point (c), between the times series of ranks R HPL
and R RTPL
.
2. Institutions shall produce the time series of ranks referred to in paragraph 1, point (b), from an originating time series by performing the following steps in the following order:
(a)
for each observation within the originating time series, institutions shall count the number of observations with a lower value than that observation within that time series;
(b)
institutions shall label each observation with the number resulting from the calculation set out in point (a) increased by one;
(c)
where, as a result of the labelling in accordance with point (b), two or more observations are labelled with the same number, institutions shall in addition increase the numbers of those labels with the following fraction:
where N equals the quantity of the labels with the same number;
(d)
institutions shall consider as time series of ranks, the time series of the labels obtained in accordance with points (b) and (c).
3. Institutions shall calculate the standard deviation of the time series of ranks R HPL
in accordance with the formula laid down in point (a), the standard deviation of the time series of ranks R RTPL
in accordance with the formula laid down in point (b), and the covariance between those time series in accordance with the formula laid down in point (c) as follows:
(a)
;
(b)
;
(c)
; Where:
i
=
the index that denotes the observation in the time series of ranks;
=
the ‘i-th’ observation of the time series of ranks R
HPL
;
=
the mean of the time series of ranks R HPL
;
=
the ‘i-th’ observation of the time series of ranks R RTPL
;
=
the mean of the time series of ranks R RTPL
.
Calculation of the Kolmogorov-Smirnov test metric
1. Institutions shall calculate the Kolmogorov-Smirnov test metric referred to in Article 6(1) of this Regulation by performing the following steps in the following order:
(a)
they shall determine the time series of the most recent 250 business days of observations of the hypothetical and theoretical changes in the trading desk portfolio’s value;
(b)
they shall calculate the empirical cumulative distribution function of the hypothetical changes in the trading desk portfolio’s value from the time series of the hypothetical changes referred to in point (a);
(c)
they shall calculate the empirical cumulative distribution function of the theoretical changes in the trading desk portfolio’s value from the time series of the theoretical changes referred to in point (a);
(d)
they shall obtain the Kolmogorov-Smirnov test metric by calculating the maximum difference between the two empirical cumulative distributions calculated in accordance with points (b) and (c) at any possible value of profit and loss.
2. For the purposes of paragraph 1, the empirical distribution function obtained from a time series shall be understood as the function that, given any number as input, results in the ratio of the number of observations within the time series with lower or equal value than the input number to the total number of observations within the time series.
Specification of criteria necessary to ensure that the theoretical changes and the hypothetical changes in the value of a trading desk portfolio are sufficiently close
1. For the purposes of Article 325bg(2) of Regulation (EU) No 575/2013, institutions shall classify each of the trading desks as a green, orange, yellow or red zone desk in accordance with paragraphs 2 to 5.
Where a trading desk is classified as a green zone desk, theoretical changes and the hypothetical changes in the value of that trading desk’s portfolio shall be considered sufficiently close.
Where a trading desk is classified as an orange, yellow or red zone desk, theoretical changes and the hypothetical changes in the value of that trading desk’s portfolio shall not be considered sufficiently close.
2. A trading desk shall be classified as a ‘green zone desk’ where all of the following conditions are met:
(a)
the Spearman correlation coefficient for the trading desk, calculated in accordance with Article 7 of this Regulation, is greater than 0,8;
(b)
the Kolmogorov-Smirnov test metric for the trading desk, calculated in accordance with Article 8 of this Regulation, is lower than 0,09.
3. A trading desk shall be classified as a ‘red zone desk’ where either of the following conditions is met:
(a)
the Spearman correlation coefficient for the trading desk, calculated in accordance with Article 7 of this Regulation, is lower than 0,7;
(b)
the Kolmogorov-Smirnov test metric for the trading desk, calculated in accordance with Article 8 of this Regulation, is greater than 0,12.
4. A trading desk shall be classified as an ‘orange zone’ desk where all of the following conditions are met:
(a)
the trading desk is not classified as either a green or a red zone desk;
(b)
the own funds requirements for all the positions assigned to that trading desk were calculated in the previous quarter based on the alternative standardised approach set out in Part Three, Title IV, Chapter 1a of Regulation (EU) No 575/2013.
5. A trading desk which is not classified as a green, orange or red zone desk, shall be classified as a ‘yellow zone desk’.
Consequences for trading desks that are classified as yellow, orange or red zone desks
1. Institutions calculating the own funds requirements in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013 for positions assigned to trading desks that have been classified as red, orange or yellow zone desks in accordance with Article 9 of this Regulation shall calculate, in relation to those positions, a capital surcharge in accordance with the following formula:
Where:
k
=
as specified in paragraph 2;
SA ima
=
the own funds requirements for market risks calculated in accordance with the alternative standardised approach set out in Part Three, Title IV, Chapter 1a of Regulation (EU) No 575/2013 for the portfolio of all positions assigned to trading desks for which the institution calculates the own funds requirements for market risks in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013;
IMA ima
=
the own funds requirements for market risks calculated in accordance the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013 for the portfolio of all positions assigned to trading desks for which the institution calculates the own funds requirements in accordance with Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013.
2. For the purposes of paragraph 1, the coefficient k shall be calculated in accordance with the following formula:
Where:
SA
i
=
the own funds requirements for market risks calculated in accordance with the alternative standardised approach set out in Part Three, Title IV, Chapter 1a of Regulation (EU) No 575/2013 for all the positions attributed to trading desk ‘I’;
=
the indices of all trading desks that have been classified as red, orange or yellow zone desks in accordance with Article 9 of this Regulation among those for which the own funds requirements for market risks are calculated in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013;
=
the indices of all trading desks for which the own funds requirements for market risks are calculated in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013.
3. Institutions calculating the own funds requirements for market risks in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013 for positions assigned to trading desks that have been classified as red or orange zone desks in accordance with Article 9 of this Regulation shall inform the competent authority thereof when reporting the results of the profit and loss attribution requirement in accordance with Article 325az(2), point (d), of Regulation (EU) No 2013/575.
Frequency of the assessment of compliance with the profit and loss attribution requirement
Institutions shall assess compliance with the profit and loss attribution requirement on a quarterly basis for all trading desks for which those institutions have the permission referred to in Article 325az(2) of Regulation (EU) No 575/2013 to calculate the own funds requirements using internal models.
Source: EUR-Lex (Publications Office of the EU), © European Union, reuse permitted under Commission Decision 2011/833/EU.
