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Capital Requirements Regulation (CRR)
Article 279a

Article 279a — Supervisory delta

  1. Institutions shall calculate the supervisory delta as follows:
    1. for call and put options that entitle the option buyer to purchase or sell an underlying instrument at a positive price on a single or multiple dates in the future, except where those options are mapped to the interest rate risk category, institutions shall use the following formula:

      $${\delta} = {\mathrm{sign} \cdot N \left (\mathrm{type} \cdot \frac{\ln (P / K) + 0,5 \cdot \sigma ^{2} \cdot T}{\sigma \cdot \sqrt{{T}}}\right )}$$

      where:

      • δ = the supervisory delta;
      • sign = – 1 where the transaction is a sold call option or a bought put option;
      • sign = + 1 where the transaction is a bought call option or sold put option;
      • type = – 1 where the transaction is a put option;
      • type = + 1 where the transaction is a call option;
      • N(x) = the cumulative distribution function for a standard normal random variable meaning the probability that a normal random variable with mean zero and variance of one is less than or equal to x;
      • P = the spot or forward price of the underlying instrument of the option; for options the cash flows of which depend on an average value of the price of the underlying instrument, P shall be equal to the average value at the calculation date;
      • K = the strike price of the option;
      • T = the expiry date of the option; for options which can be exercised at one future date only, the expiry date is equal to that date; for options which can be exercised at multiple future dates, the expiry date is equal to the latest of those dates; the expiry date shall be expressed in years using the relevant business day convention; and
      • σ = the supervisory volatility of the option determined in accordance with Table 1 on the basis of the risk category of the transaction and the nature of the underlying instrument of the option.

      Table 1
      Risk categoryUnderlying instrumentSupervisory volatility
      Foreign exchangeAll15 %
      CreditSingle-name instrument100 %
      Multiple-names instrument80 %
      EquitySingle-name instrument120 %
      Multiple-names instrument75 %
      CommodityElectricity150 %
      Other commodities (excluding electricity)70 %
      OthersAll150 %

      Institutions using the forward price of the underlying instrument of an option shall ensure that:

      1. the forward price is consistent with the characteristics of the option;
      2. the forward price is calculated using a relevant interest rate prevailing at the reporting date;
      3. the forward price integrates the expected cash flows of the underlying instrument before the expiry of the option;
    2. for tranches of a synthetic securitisation and a nth-to-default credit derivative, institutions shall use the following formula:

      $${\delta} = {\mathrm{sign} \cdot \frac{15}{(1 + 14 \cdot A) \cdot (1 + 14 \cdot D)}}$$

      where:

      sign = + 1 where credit protection has been obtained through the transaction
      – 1 where credit protection has been provided through the transaction

      • A = the attachment point of the tranche; for a nth-to-default credit derivative transaction based on reference entities k, A = (n – 1)/k; and
      • D = the detachment point of the tranche; for a nth-to-default credit derivative transaction based on reference entities k, D = n/k;
    3. for transactions not referred to in point (a) or (b), institutions shall use the following supervisory delta:

      δ = + 1 if the transaction is a long position in the primary risk driver or in the most material risk driver in the given risk category
      – 1 if the transaction is a short position in the primary risk driver or in the most material risk driver in the given risk category
  2. For the purposes of this Section, a long position in the primary risk driver or in the most material risk driver in the given risk category for transactions referred to in Article 277(3) means that the market value of the transaction increases when the value of that risk driver increases and a short position in the primary risk driver or in the most material risk driver in the given risk category for transactions referred to in Article 277(3) means that the market value of the transaction decreases when the value of that risk driver increases.
  3. EBA shall develop draft regulatory technical standards to specify:
    1. in accordance with international regulatory developments, the formula that institutions shall use to calculate the supervisory delta of call and put options mapped to the interest rate risk category compatible with market conditions in which interest rates may be negative as well as the supervisory volatility that is suitable for that formula;
    2. the method for determining whether a transaction is a long or short position in the primary risk driver or in the most material risk driver in the given risk category for transactions referred to in Article 277(3).

    EBA shall submit those draft regulatory technical standards to the Commission by 28 December 2019.

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