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  • CA-8.3 CA-8.3 Delta-plus method (buffer approach)

    • CA-8.3.1

      Banks which write options are allowed to include delta-weighted option positions within the standardised methodology set out in Chapters CA-4 through CA-7. Each option should be reported as a position equal to the market value of the underlying multiplied by the delta. The delta should be calculated by an adequate model with appropriate documentation of the process and controls, to enable the Central Bank to review such models, if considered necessary. A worked example of the delta-plus method is set out in Appendix CA-6.

      October 07

    • CA-8.3.2

      Since delta does not sufficiently cover the risks associated with options positions, there will be additional capital buffers to cover gamma (which measures the rate of change of delta) and vega (which measures the sensitivity of the value of an option with respect to a change in volatility), in order to calculate the total capital charge. The gamma and vega buffers should be calculated by an adequate exchange model or the bank's proprietary options pricing model, with appropriate documentation of the process and controls, to enable the Central Bank to review such models, if considered necessary.

      October 07

    • Treatment of delta

      • CA-8.3.3

        The treatment of the delta-weighted positions, for the calculation of the capital charges arising from delta risk, is summarised in Paragraphs CA-8.3.4 to CA-8.3.9.

        October 07

    • Where the underlying is a debt security or an interest rate

      • CA-8.3.4

        The delta-weighted option positions are slotted into the interest rate time-bands as set out in Chapter CA-4. A two-legged approach should be used as for other derivatives, as explained in Chapter CA-4, requiring one entry at the time the underlying contract takes effect and a second at the time the underlying contract matures. A few examples to elucidate the two-legged treatment are set out below:

        (a) A bought call option on a June three-month interest rate future will, in April, be considered, on the basis of its delta-equivalent value, to be a long position with a maturity of five months and a short position with a maturity of two months.
        (b) A written option with the same underlying as in (a) above, will be included in the measurement framework as a long position with a maturity of two months and a short position with a maturity of five months.
        (c) A two months call option on a bond future where delivery of the bond takes place in September will be considered in April, as being long the bond and short a five months deposit, both positions being delta-weighted.
        October 07

      • CA-8.3.5

        Floating rate instruments with caps or floors are treated as a combination of floating rate securities and a series of European-style options. For example, the holder of a three-year floating rate bond indexed to six month LIBOR with a cap of 10% will treat it as:

        (a) A debt security that reprices in six months; and
        (b) A series of five written call options on an FRA with a reference rate of 10%, each with a negative sign at the time the underlying FRA takes effect and a positive sign at the time the underlying FRA matures.
        October 07

      • CA-8.3.6

        The rules applying to closely matched positions, set out in Paragraph CA-4.8.2, will also apply in this respect.

        October 07

    • Where the underlying is an equity instrument

      • CA-8.3.7

        The delta-weighted positions are incorporated in the measure of market risk described in Chapter CA-5. For purposes of this calculation, each national market is treated as a separate underlying.

        October 07

    • Options on foreign exchange and gold positions

      • CA-8.3.8

        The net delta-based equivalent of the foreign currency and gold options are incorporated in the measurement of the exposure for the respective currency or gold position, as described in Chapter CA-6.

        October 07

    • Options on commodities

      • CA-8.3.9

        The delta-weighted positions are incorporated in the measurement of the commodities risk by the simplified approach or the maturity ladder approach, as described in Chapter CA-7.

        October 07

    • Calculation of the gamma and vega buffers

      • CA-8.3.10

        As explained in Paragraph CA-8.3.2, 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 × Gamma × 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 options18, where the underlying is a bond, the market value of the underlying is multiplied by the risk weights set out in Section CA-4.4. 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-4.5;
        (ii) For options on equities and equity indices18, 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-4.4. 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-4.5;
        (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-7.2.
        (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%.
        (g) The total vega capital charge is the sum of the absolute value of the individual vega capital charges calculated for each underlying.

        18 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-8.4 for an explanation of the Central Bank's views on this subject.

        October 07

      • CA-8.3.11

        The capital charges for delta, gamma and vega risks described in Paragraphs CA-8.3.1 through CA-8.3.10 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-4 through CA-7.

        October 07

      • CA-8.3.12

        To summarise, capital requirements for, say OTC options, using 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-8.3.11); PLUS
        (c) Delta risk capital charges (calculated as explained in Paragraphs CA-8.3.3 through CA-8.3.9) PLUS
        (d) Gamma and vega capital buffers (calculated as explained in Paragraph CA-8.3.10).
        October 07