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  • Calculation of the Gamma and Vega Buffers

    • CA-13.3.10

      As explained in Paragraph CA-13.3.2, in addition to the above capital charges to cover delta risk, banks are required to calculate additional capital charges to cover the gamma and vega risks. The additional capital charges are calculated as follows:

      Gamma

      (a) For each individual option position (including hedge positions), a gamma impact is calculated according to the following formula derived from the Taylor series expansion:

      Gamma impact = 0.5 x Gamma x VU

      where VU = variation of the underlying of the option, calculated as in (b) below
      (b) VU is calculated as follows:
      (i) For interest rate options79, where the underlying is a bond, the market value of the underlying is multiplied by the risk weights set out in Section CA-9.4. An equivalent calculation is carried out where the underlying is an interest rate, based on the assumed changes in yield as set out in the table in Section CA-9.5;
      (ii) For options on equities and equity indices, the market value of the underlying is multiplied by 8%;
      (iii) For foreign exchange and gold options, the market value of the underlying is multiplied by 8%;
      (iv) For commodities options, the market value of the underlying is multiplied by 15%.
      (c) For the purpose of the calculation of the gamma buffer, the following positions are treated as the same underlying:
      (i) For interest rates, each time-band as set out in the table in Section CA-9.4. Positions should be slotted into separate maturity ladders by currency. Banks using the duration method should use the time-bands as set out in the table in Section CA-9.5;
      (ii) For equities and stock indices, each individual national market;
      (iii) For foreign currencies and gold, each currency pair and gold; and
      (iv) For commodities, each individual commodity as defined in Section CA-12.2.
      (d) Each option on the same underlying will have a gamma impact that is either positive or negative. These individual gamma impacts are summed, resulting in a net gamma impact for each underlying that is either positive or negative. Only those net gamma impacts that are negative are included in the capital calculation;
      (e) The total gamma capital charge is the sum of the absolute value of the net negative gamma impacts calculated for each underlying as explained in (d) above;

      Vega

      (f) For volatility risk (vega), banks are required to calculate the capital charges by multiplying the sum of the vegas for all options on the same underlying, as defined above, by a proportional shift in volatility of ±25%; and
      (g) The total vega capital charge is the sum of the absolute value of the individual vega capital charges calculated for each underlying.

      79 For interest rate and equity options, the present set of rules do not attempt to capture specific risk when calculating gamma capital Charges. See Section CA-13.4 for an explanation of the CBB's views on this subject.

      Amended: January 2012
      Amended: April 2011
      Apr 08

    • CA-13.3.11

      The capital charges for delta, gamma and vega risks described in Paragraphs CA-13.3.1 through CA-13.3.10 are in addition to the specific risk capital charges which are determined separately by multiplying the delta-equivalent of each option position by the specific risk weights set out in chapters CA-9 through CA-12.

      Amended: January 2012
      Apr 08

    • CA-13.3.12

      To summarise, capital requirements for, say OTC options, applying the delta-plus method are as follows:

      (a) Counterparty risk capital charges (on purchased options only), calculated in accordance with the credit risk regulations; PLUS
      (b) Specific risk capital charges (calculated as explained in Paragraph CA-13.3.11); PLUS
      (c) Delta risk capital charges (calculated as explained in Paragraphs CA-13.3.3 through CA-13.3.9) PLUS
      (d) Gamma and vega capital buffers (calculated as explained in Paragraph CA-13.3.10).
      Amended: January 2012
      Apr 08