Capital Requirements Regulation (CRR)

### Article 383 — Advanced method

1. An institution which has permission to use an internal model for the specific risk of debt instruments in accordance with point (d) of Article 363 (1) shall, for all transactions for which it has permission to use the IMM for determining the exposure value for the associated counterparty credit risk exposure in accordance with Article 283, determine the own funds requirements for CVA risk by modelling the impact of changes in the counterparties' credit spreads on the CVAs of all counterparties of those transactions, taking into account CVA hedges that are eligible in accordance with Article 386.

An institution shall use its internal model for determining the own funds requirements for the specific risk associated with traded debt positions and shall apply a 99 % confidence interval and a 10-day equivalent holding period. The internal model shall be used in such way that it simulates changes in the credit spreads of counterparties, but does not model the sensitivity of CVA to changes in other market factors, including changes in the value of the reference asset, commodity, currency or interest rate of a derivative.

The own funds requirements for CVA risk for each counterparty shall be calculated in accordance with the following formula:

$${\mathrm{CVA}} = {\mathrm{LGD} _{\mathrm{MKT}} \cdot \sum \max \left \{0,exp \left (- {\frac{s _{i - 1} \cdot t _{i - 1}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right ) - \exp \left (- {\frac{s _{i} \cdot t _{i}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right )\right \} \cdot {\frac{\mathrm{EE} _{i - 1} \cdot D _{i - 1} + \mathrm{EE} _{i} \cdot D _{i}}{2}}}$$

where:

ti = the time of the i-th revaluation, starting from t0=0;tT = the longest contractual maturity across the netting sets with the counterparty;si = is the credit spread of the counterparty at tenor ti, used to calculate the CVA of the counterparty. Where the credit default swap spread of the counterparty is available, an institution shall use that spread. Where such a credit default swap spread is not available, an institution shall use a proxy spread that is appropriate having regard to the rating, industry and region of the counterparty;LGDMKT = the LGD of the counterparty that shall be based on the spread of a market instrument of the counterparty if a counterparty instrument is available. Where a counterparty instrument is not available, it shall be based on the proxy spread that is appropriate having regard to the rating, industry and region of the counterparty.

The first factor within the sum represents an approximation of the market implied marginal probability of a default occurring between times ti-1 and ti;

2. When calculating the own funds requirements for CVA risk for a counterparty, an institution shall base all inputs into its internal model for specific risk of debt instruments on the following formulae (whichever is appropriate):
1. where the model is based on full repricing, the formula in paragraph 1 shall be used directly;
2. where the model is based on credit spread sensitivities for specific tenors, an institution shall base each credit spread sensitivity ('Regulatory CS01') on the following formula:

$${Regulatory CS01 _{i}} = {0.0001 \cdot t _{i} \cdot \exp \left (- {\frac{s _{i} \cdot t _{i}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right ) \cdot {\frac{\mathrm{EE} _{i - 1} \cdot D _{i - 1} - \mathrm{EE} _{i + 1} \cdot D _{i + 1}}{2}}}$$

For the final time bucket i=T, the corresponding formula is

$${Regulatory CS01 _{T}} = {0.0001 \cdot t _{T} \cdot \exp \left (- {\frac{s _{T} \cdot t _{T}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right ) \cdot {\frac{\mathrm{EE} _{T - 1} \cdot D _{T - 1} + \mathrm{EE} _{T} \cdot D _{T}}{2}}}$$
3. where the model uses credit spread sensitivities to parallel shifts in credit spreads, an institution shall use the following formula:

$${Regulatory CS01} = {{{0.0001 \cdot \sum \left ({t _{i} \cdot \exp \left (- {\frac{s _{i} \cdot t _{i}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right )} - {t _{i - 1} \cdot \exp \left (- {\frac{s _{i - 1} \cdot t _{i - 1}}{\mathrm{LGD} _{\mathrm{MKT}}}}\right )}\right ) \cdot {\frac{{\mathrm{EE} _{i - 1} \cdot D _{i - 1}} + {\mathrm{EE} _{i} \cdot D _{i}}}{2}}}}}$$
4. where the model uses second-order sensitivities to shifts in credit spreads (spread gamma), the gammas shall be calculated based on the formula in paragraph 1.
3. An institution using the EPE measure for collateralised OTC derivatives referred to in point (a) or (b) of Article 285(1) shall, when determining the own funds requirements for CVA risk in accordance with paragraph 1, do both of the following:
1. assume a constant EE profile;
2. set EE equal to the effective expected exposure as calculated under Article 285(1)(b) for a maturity equal to the greater of the following:
1. half of the longest maturity occurring in the netting set;
2. the notional weighted average maturity of all transactions inside the netting set.
4. An institution which is permitted by the competent authority in accordance with Article 283 to use IMM to calculate exposure values in relation to the majority of its business, but which uses the methods set out in Section 3, Section 4 or Section 5 of Title II, Chapter 6 for smaller portfolios, and which has permission to use the market risk internal model for the specific risk of debt instruments in accordance with point (d) of Article 363(1) may, subject to permission from the competent authorities, calculate the own funds requirements for CVA risk in accordance with paragraph 1 for the non-IMM netting sets. Competent authorities shall grant this permission only if the institution uses the methods set out in Section 3, Section 4 or Section 5 of Title II, Chapter 6 for a limited number of smaller portfolios.

For the purposes of a calculation under the preceding subparagraph and where the IMM model does not produce an expected exposure profile, an institution shall do both of the following:

1. assume a constant EE profile;
2. set EE equal to the exposure value as computed under the methods set out in Section 3, Section 4 or Section 5 of Title II, Chapter 6, or IMM for a maturity equal to the greater of:
1. half of the longest maturity occurring in the netting set;
2. the notional weighted average maturity of all transactions inside the netting set.
5. An institution shall determine the own funds requirements for CVA risk in accordance with Article 364(1) and Articles 365 and 367 as the sum of non-stressed and stressed value-at-risk, which shall be calculated as follows:
1. for the non-stressed value-at-risk, current parameter calibrations for expected exposure as set out in the first subparagraph of Article 292(2), shall be used;
2. for the stressed value-at-risk, future counterparty EE profiles using a stressed calibration as set out in the second subparagraph of Article 292(2) shall be used. The period of stress for the credit spread parameters shall be the most severe one-year stress period contained within the three-year stress period used for the exposure parameters;
3. the three-times multiplication factor used in the calculation of own funds requirements based on a value-at-risk and a stressed value-at-risk in accordance with 364(1) will apply to these calculations. EBA shall monitor for consistency any supervisory discretion used to apply a higher multiplication factor than that three-times multiplication factor to the value-at-risk and stressed value-at-risk inputs to the CVA risk charge. Competent authorities applying a multiplication factor higher than three shall provide a written justification to EBA;
4. the calculation shall be carried out on at least a monthly basis and the EE that is used shall be calculated on the same frequency. If lower than a daily frequency is used, for the purpose of the calculation specified in points (a)(ii) and (b)(ii)(b)(ii) of Article 364(1) institutions shall take the average over three months.
6. For exposures to a counterparty, for which the institution's approved internal model for the specific risk of debt instruments does not produce a proxy spread that is appropriate with respect to the criteria of rating, industry and region of the counterparty, the institution shall use the method set out in Article 384 to calculate the own funds requirement for CVA risk.
7. EBA shall develop draft regulatory technical standards to specify in greater detail:
1. how a proxy spread is to be determined by the institution's approved internal model for the specific risk of debt instruments for the purposes of identifying si and LGDMKT referred to in paragraph 1;
2. the number and size of portfolios that fulfil the criterion of a limited number of smaller portfolios referred to in paragraph 4.

EBA shall submit those draft regulatory technical standards to the Commission by 1 January 2014.

Power is delegated to the Commission to adopt the regulatory technical standards referred to in the first subparagraph in accordance with Articles 10 to 14 of Regulation (EU) No 1093/2010.