## PRU A6.6 PRU A6.6 Option Risk Capital Requirement

## Guidance

Section A6.6 presents the method for the calculation of Option Risk Capital Requirement for the purpose of Rule 5.8.1(b).

## PRU A6.6.1

An Authorised Person which calculates its Option Risk Capital Requirement in accordance with Rule 5.8.1(b) must apply the Rules in this Section.

## Calculation of Option Risk Capital Requirement

## PRU A6.6.2

(1) An Authorised Person may use the Simplified Approach set out in Rule A6.6.3 to calculate its Option Risk Capital Requirement only if:(a) it does not write Options; or(b) where it writes Options, all written Options are hedged by perfectly matched long positions in exactly the same Options.(2) An Authorised Person which writes Options must, unless (1) applies, use the advanced approach known as the Delta-plus method set out in Rule A6.6.5 to calculate its Option Risk Capital Requirement.## Simplified Approach

## PRU A6.6.3 PRU A6.6.3

An Authorised Person using the Simplified Approach must treat the positions for the Options and the associated underlying instrument, cash or forward, and calculate the capital charge for each position, by reference to the following table:

**Position****Treatment**Long cash and long put or short cash and long call. The capital charge is the market value of the underlying instrument multiplied by the sum of Specific and General Market Risk percentages for the underlying Instrument less the amount the Option is in the money, if any, bounded at zero. Long call or long put. The capital charge will be the lesser of: • the market value of the underlying instrument multiplied by the sum of Specific and General Market Risk percentages for the underlying instrument; or• the market value of the Options.## Guidance

As an example of how the calculation would work, if a holder of 100 Shares currently valued at $10 each holds an equivalent put Option with a strike price of $11, the capital charge would be: $1,000 × 16% (i.e., 8% specific plus 8% General Market Risk) = $160, less the amount the Option is in the money ($11 - $10) × 100 = $100, i.e., the capital charge would be $60. A similar methodology applies for Options whose underlying instrument is a Foreign Currency, an interest rate related instrument or a commodity.

## PRU A6.6.4

(1) For the purposes of Rule A6.6.3, the Specific Risk percentage for:(a) a currency Option is 8%; and(b) an Option on commodities is 15%.(2) For the purposes of Rule A6.6.3, in the case of an Option with a residual maturity of more than six months, the strike price must be compared with the forward, not current price, or if the Authorised Person is unable to do this, then the Money amount must be taken to be zero.## Delta-plus method

## Guidance

The 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 5.4 to 5.7 with the Delta-equivalent amount subject to the applicable General Market Risk requirements. Separate capital charges are then applied to the Gamma and Vega risks of the Option positions.

## PRU A6.6.5

(1) An Authorised Person that writes or purchases Options may include Delta-weighted Options positions within the standardised methodology set out in Sections A6.2 to A6.5. Such Options must be reported as a position equal to the market value of the underlying instrument multiplied by the Delta.(2) An Authorised Person is also required to measure and Vega risks 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 Securities or interest rates as the underlying instrument must be inserted into the interest rate timebands, as set out in Section A6.2. 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 Securities and 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 Requirement described in Section A6.3. 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 Section 5.8. For Delta risk, the net Delta-based equivalent of the commodities, foreign currency including gold) Options must be incorporated into the measurement of the Exposure for the respective currency (or gold) position.## PRU A6.6.6

An Authorised Person using the Delta-plus method must calculate its Market Risk Capital Requirement for Options by:

(a) calculating the Delta-weighted position of each Option in accordance with Rule A6.6.7 and adding these Delta-weighted positions to the net positions in the relevant risk category referred in Sections A6.2 to A6.6 for the purpose of calculating the Specific Risk and General Market Risk Capital Requirements;(b) calculating the Capital Requirement for Gamma risk of its Option positions (including hedge positions) based on the Options pricing model of the an Authorised Person, in accordance with Rules A6.6.8 to A6.6.9;(c) calculating the Capital Requirement for Vega risk of its Option positions (including hedge positions) based on the Options pricing model of an Authorised Person, in accordance with Rule A6.6.10; and(d) summing the Capital Requirements determined in (b) and (c).## PRU A6.6.7

An Authorised Person must calculate its Delta-weighted position for each Option as follows:

Delta-weighted position = Market value of the underlying instrument or commodities × Delta## PRU A6.6.8

In addition to the capital charges referred to in Rule A6.6.5, arising from Delta risk, an Authorised Person must calculate the Gamma for each Option position, including hedge positions in the following way:

(a) for each individual Option a "Gamma impact" must be calculated as:Gamma impact = ½ × Gamma × VU^{2}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 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 Rule A6.2.16;(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 Rule A6.2.16;(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 Section A6.5 for Commodities Risk Capital Requirement.## PRU A6.6.9 PRU A6.6.9

An Authorised Person must calculate its Capital Requirement for Gamma risk by:

(a) calculating the net Gamma impact in respect of each underlying Financial Instrument or commodity by aggregating the individual Gamma impacts 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 Gamma impacts that are negative.## Guidance

1. 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 Section A6.2;b. the specific and general risk weights in respect of Options on equities and equity indices are determined in accordance with Section A6.3;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 six months, the strike price should be compared with the forward, and not current, price. Where an Authorised Person is unable to do this, the in-the-money amount would be zero.2. An Authorised Person which 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 Requirement for such Options, unless it is able to demonstrate to the Regulator that 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).## PRU A6.6.10

An Authorised Person must calculate its Capital Requirement for Vega risk by:

(a) multiplying the sum of the Vegas for all Option positions in respect of the same underlying Financial Instrument or commodity, as defined in the Rule 5.6.8(c), by a proportional shift in volatility of ±25%; and(b) aggregating the absolute value of the individual Capital Requirements which have been calculated for Vega risk.