Delta-Plus Method Guidance
Delta-plus method uses the sensitivity parameters or "Greek letters" associated with options to measure their Option Risk Capital Requirement. Under this method, the Delta-equivalent position of each option becomes part of the standardised methodology set out in sections PIB 5.4 to PIB 5.7 with the Delta-equivalent amount subject to the applicable General Market Riskrequirements. Separate capital charges are then applied to the Gammaand Vegarisks of the option positions.
PIB A5.6.5(1) An
Authorised Firmthat writes or purchases options may include Delta-weighted options positions within the standardised methodology set out in sections PIB A5.2 to PIB A5.5. Such options must be reported as a position equal to the market value of the underlying instrument multiplied by the Delta.(2) An Authorised Firmis also required to measure and Vegarisks in order to calculate the total capital charge. These sensitivities will be calculated according to an approved proprietary options pricing model.(3) Delta-weighted positions with debt Securitiesor interest rates as the underlying instrument must be inserted into the interest rate timebands, as set out in PIB section A5.2. A two-legged approach must be used as for other derivatives, requiring one entry at the time the underlying instrument takes effect and a second at the time the underlying instrument matures. Floating rate instruments with caps or floors must be treated as a combination of floating rate Securitiesand a series of European-style options.(4) The capital charge for options with equities as the underlying instrument must also be based on the Delta-weighted positions which must be incorporated in the measure of Equity Risk Capital Requirementdescribed in PIB section A5.3. For purposes of this calculation, each national market must be treated as a separate underlying instrument.(5) The capital charge for options on commodities, foreign currency (including gold) positions must be based on the method set out in PIB section 5.8. For Deltarisk, the net Delta-based equivalent of the commodities, foreign currency including gold) options must be incorporated into the measurement of the Exposurefor the respective currency (or gold) position.(6) Individual net Deltapositions as described above must be treated as the underlying instrument in accordance with sections PIB A5.4 to PIB A5.5.
Authorised Firmusing the Delta-plus method must calculate its Market Risk Capital Requirementfor options by:(a) calculating the Delta-weighted position of each option in accordance with PIB Rule A5.6.7 and adding these Delta-weighted positions to the net positions in the relevant risk category referred in sections PIB A5.2 to PIB A5.6 for the purpose of calculating the Specific Riskand General Market Risk Capital Requirements;(b) calculating the Capital Requirementfor Gammarisk of its option positions (including hedge positions) based on the options pricing model of the an Authorised Firm, in accordance with Rules PIB A5.6.8 to PIB A5.6.9;(c) calculating the Capital Requirementfor Vegarisk of its option positions (including hedge positions) based on the options pricing model of an Authorised Firm, in accordance with PIB Rule A5.6.10; and(d) summing the Capital Requirementsdetermined in (b) and (c).
Authorised Firmmust calculate its Delta-weighted position for each option as follows: Delta-weighted position = Market value of the underlying instrument or commodities x Delta
In addition to the capital charges referred to in PIB Rule A5.6.5, arising from
Deltarisk, an Authorised Firmmust calculate the Gammafor each option position, including hedge positions in the following way:(a) for each individual option a " Gammaimpact" must be calculated as:
Gammaimpact = ½ x Gammax VU2
where VU = Variation of the underlying instrument of the option;(b) VU must be calculated as follows:(i) for interest rate options if the underlying instrument is a bond, the market value of the underlying instrument should be multiplied by the risk weights set out in PIB section 5.4 for the underlying instrument. An equivalent calculation should be carried out where the underlying instrument is an interest rate, again based on the assumed changes in the corresponding yield in PIB Rule A5.2.16;(ii) for options on equities and equity indices, the market value of the underlying instrument should be multiplied by 8%;(iii) for foreign exchange and gold options, the market value of the underlying instrument should be multiplied by 8%; and(iv) for options on commodities, the market value of the underlying instrument should be multiplied by 15%; and(c) for the purpose of this calculation the following positions must be treated as the same underlying instrument:(i) for interest rates, each timeband as set out in PIB Rule A5.2.16;(ii) for equities and stock indices, each national market;(iii) for foreign currencies and gold, each currency pair and gold; and(iv) for commodities, positions in the same individual commodity as defined in PIB section A5.5 for
Commodities Risk Capital Requirement.
PIB A5.6.9 PIB A5.6.9
Authorised Firmmust calculate its Capital Requirementfor Gammarisk by:(a) calculating the net Gammaimpact in respect of each underlying financial instrument or commodity by aggregating the individual Gammaimpacts for each option position in respect of that underlying financial instrument or commodity (which may be either positive or negative); and(b) aggregating the absolute value of the net Gammaimpacts that are negative.
PIB A5.6.9 Guidance1. The underlying financial instrument or commodity should be taken to be the asset which would be received if the option were exercised. In addition, the notional value should be used for items where the market value of the underlying financial instrument or commodity could be zero (e.g. caps and floors, swaptions). Certain notional positions in zero-specific-risk securities do not attract
Specific Risk, e.g. interest rate and currency swaps, Forward Rate Agreement (FRA), forward foreign exchange contracts, interest rate futures and futures on an interest rate index. Similarly, options on such zero-specific-risk securities also bear no Specific Risk. For the purposes of this sub-paragraph:a. the specific and general risk weights in respect of options on interest rate-related instruments are determined in accordance with PIB section A5.2;b. the specific and general risk weights in respect of options on equities and equity indices are determined in accordance with PIB section A5.3;c. the risk weight in respect of foreign currency and gold options is 8%; andd. the risk weight in respect of options on commodities is 15%.For options with a residual maturity of more than 6 months, the strike price should be compared with the forward, and not current, price. Where an Authorised Firmis unable to do this, the in-the-money amount would be zero.2. An Authorised Firmwhich trades in exotic options (e.g. barriers, digitals) would use either the scenario approach or the Internal Models Approach(IMA) to calculate its Market Risk Capital Requirementfor such options, unless it is able to demonstrate to the DFSAthat the Delta-plus method is appropriate. In the case of options on futures or forwards, the relevant underlying is that on which the future or forward is based (e.g. for a bought call option on a June 3-month bill future, the relevant underlying is the 3-month bill).
Authorised Firmsmust calculate its Capital Requirementfor Vegarisk by:(a) multiplying the sum of the Vegasfor all option positions in respect of the same underlying financial instrument or commodity, as defined in the PIB Rule 5.6.8(c), by a proportional shift in volatility of ±25%; and(b) aggregating the absolute value of the individual Capital Requirementswhich have been calculated for Vegarisk.