| (1) | A bank that writes options shall include delta-weighted option positions in the standardised methodology set out in regulation 13, read with regulations 14 and 15. These options shall be reported as a position equal to the market value of the underlying instrument multiplied by the delta. Since the delta does not sufficiently cover the risks associated with option positions, the bank shall in addition measure the gamma sensitivity (which measures the rate of change of delta) and the vega sensitivity (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. These sensitivity analyses shall be calculated according to an approved model or according to the bank's proprietary options valuation model, subject to the prior written approval of the Registrar. |
| (2) | Delta-weighted positions on debt securities, or interest rates as the underlying instrument, shall be included in the interest-rate time bands, as set out in regulation 15, in accordance with the following procedure: |
| (a) | Delta-weighted positions shall include other derivatives, requiring one entry at the time at which the underlying contract takes effect and a second entry at the time at which the underlying contract matures. (For example, in the case of a broad call option on a June three-month interest-rate future, this option will be valued in April on the basis of its delta-equivalent as a long position with a maturity of five months and as a short position with a maturity of two months); |
| (b) | a option shall similarly be regarded as a long position with a maturity of two months and a short position with a maturity of five months in the same example; and |
| (c) | floating-rate instruments with caps or floors shall be 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 months LIBOR with a cap of 15 per cent shall be treated as a debt security that reprices in six months' time and as a series of five written call options on a forward rate agreement with a reference rate of 15 per cent, each having a negative sign at the time at which the underlying forward rate agreement takes effect, and a positive sign at the time at which the underlying forward rate agreement matures). |
| (3) | The capital-adequacy charge for options with equities as the underlying instruments shall also be calculated on the delta-weighted method, which shall be incorporated in the measurement of market risk described in regulation 15. For purposes of such a calculation, each market jurisdiction shall be treated separately with regard to its underlying instruments. |
| (4) | The capital-adequacy charge for options on foreign exchange and gold positions shall be based on the method set out in regulation 14. For the calculation of delta risk, the net delta-based equivalent of the foreign currency and gold options shall be incorporated into the measurement of the exposure for each currency (or gold) position. The capital-adequacy charge for options on commodities shall be based on either the simplified method or the maturity ladder method set out in regulations 14 and 15. The delta-weighted positions shall be incorporated in the measurement described in regulation 15. |
| (5) | In addition to the capital-adequacy calculation referred to in this regulation, arising from delta risk, there shall be a further capital-adequacy calculation for gamma risk and for vega risk. A bank using the delta-plus method shall calculate the gamma and vega for each option position (including hedge positions) separately. The capital-adequacy charge shall be calculated in the following manner: |
| (a) | For each individual option, a "gamma impact" shall be calculated according to a Taylor series expansion as: |
gamma impact = ½ x gamma x VU2
where VU = variation of the underlying option;
| (b) | VU shall be calculated as follows: |
| (i) | For interest-rate options when the underlying instrument is a bond, the market value of the underlying instrument shall be multiplied by the risk weighting set out in Table 4 of regulation 15. An equivalent calculation shall be performed in the case of the underlying instrument being an interest rate, based on the assumed changes in the corresponding yield in Table 5 of regulation 15; |
| (ii) | for options on equities and equity indices, the market value of the underlying instrument shall be multiplied by 8 per cent; |
| (iii) | for foreign exchange and gold options, the market value of the underlying instrument shall be multiplied by 8 per cent; and |
| (iv) | for options on commodities, the market value of the underlying instrument shall be multiplied by 15 per cent. |
| (c) | For the purpose of the calculation contemplated in this subregulation (5), the positions shall be treated as follows: |
| (i) | For interest rates, as for each time band as set out in Table 5 of regulation 15; |
| (ii) | for equities and stock indices, as for each market jurisdiction; |
| (iii) | for foreign currencies and gold, as for each currency pair and gold; and |
| (iv) | for commodities, as for each individual commodity. |
| (6) | Every option on the same underlying instrument will have a gamma impact that is either positive or negative. These individual gamma impacts shall be aggregated, resulting in a net gamma impact for each underlying instrument that is either positive or negative. The net gamma impacts that are negative shall be included in the capital-adequacy calculation. |
| (7) | The gamma capital-adequacy charge shall be the sum of the absolute value of the net negative gamma impacts calculated. |
| (8) | For volatility risk, a bank shall calculate the capital adequacy by multiplying the sum of the vegas for all options on the same underlying instrument, as defined, by a proportional shift in volatility of ± 25 per cent. |
| (9) | The total capital-adequacy charge for vega risk shall be the sum of the absolute value of the individual capital-adequacy charges calculated for vega risk. |
