(f) Matters relating to options
| (i) | For the measurement of a bank's exposure to price risk arising from option positions, a bank— |
| (A) | that solely uses purchased options or hedges all written option positions with perfectly matched long positions in exactly the same options may adopt the simplified approach specified in subparagraph (ii) below; |
| (B) | that also writes options shall adopt the delta-plus approach, scenario approach or comprehensive risk management model approach respectively specified in subparagraphs (iii) and (iv), and in subregulation (8) below, |
provided that—
| (i) | the bank shall adopt the more sophisticated approaches specified in this paragraph (f) when the bank's trading activities in options become significant or when the bank conducts business in exotic options; |
| (ii) | a bank that wishes to adopt the scenario approach or internal models approach shall obtain the prior written approval of the Registrar and shall comply with such conditions as may be specified in writing by the Registrar in addition to such conditions as may be specified in these Regulations. |
(ii) Matters relating to the simplified approach
A bank that adopted the simplified approach for the measurement of the bank's exposure to price risk arising from option positions—
| (A) | shall "carve-out" the relevant option positions and their associated underlying, irrespective whether the said positions are cash or forward positions, and separately calculate the relevant capital requirements in respect of the said positions in accordance with the relevant requirements specified in this subparagraph (ii), which requirements incorporate both general risk and specific risk, that is, instead of applying the standardised methodology envisaged in this subregulation (7) the bank shall "carve-out" all relevant option positions and associated underlying positions and separately calculate the bank's capital requirements in respect of the said positions; |
| (B) | shall add to the relevant capital requirements relating to the bank's relevant category of instruments or exposures the relevant capital requirements calculated in accordance with the relevant requirements specified in this subparagraph (ii), that is, for example, interest rate related instruments, equity instruments, foreign exchange or commodities, as the case may be, calculated in accordance with the relevant requirements specified in this subregulation (7); |
| (C) | shall, based on the relevant requirements specified in table 8 below, calculate the bank's required amount of capital and reserve funds in respect of the said option positions. |
Table 8
Simplified approach: capital requirements
Relevant position
|
Capital requirement
|
Long cash and long put
or
Short cash and long call
|
The bank's capital requirement shall be equal to the market value of the relevant underlying instrument 1, 2 multiplied by the sum of specific instrument, less the extent to which the option is in the money 3
|
Long call
or
Long put
|
The bank's capital requirement shall be equal to the lesser of:
| (i) | the market value of the underlying instrument multiplied by the sum of the specific and general risk requirements relating to the said underlying instrument; or |
| (ii) | the market value of the option. |
|
| 1. | When the market value of the underlying instrument may be zero, such as caps and floors, or swaptions, the bank shall use the relevant nominal value. |
| 2. | When it is unclear which side is the "relevant underlying instrument", such as in the case of foreign exchange, the bank shall base its calculation on the asset that will be received when the option is exercised. |
| 3. | In the case of options with a residual maturity of more than six months the bank shall compare the strike price with the forward price instead of the current price, otherwise the in-the-money amount shall be deemed to be equal to zero. |
For example, when a bank that holds 100 shares currently valued at R10 each has an equivalent put option with a strike price of R11, the bank's capital requirement shall be equal to R1,000 x 16 per cent, that is, 8 per cent specific risk plus 8 per cent general risk, which is equal to R160, less the amount the option is in the money, that is, (R11 - R10) x 100, which is equal to R100. Therefore the bank's aggregate capital requirement in respect of the said position is equal to R60.
| (iii) | Matters relating to the delta-plus approach |
A bank that adopted the delta-plus approach for the measurement of the bank's exposure to price risk arising from option positions, which approach incorporates specified sensitivity parameters associated with options—
| (A) | shall incorporate the relevant delta-weighted position relating to each relevant option position, that is, the market value of the underlying instrument multiplied with the absolute value of the relevant delta, into the relevant standardised framework specified in this subregulation (7)— |
| (i) | which standardized framework may relate to debt securities and other interest rate related instruments, equity instruments, foreign exchange risk which includes gold, or commodity risk; |
| (ii) | which delta value measures the sensitivity of the value of the option with respect to a change in the price of the underlying asset or instrument; |
| (iii) | which delta-equivalent amount, for example, shall be subject to the relevant general risk requirement; |
| (B) | shall, based on the relevant requirements specified in this subparagraph (iii), in addition to the relevant requirements for delta risk and in respect of each relevant option position, separately calculate the bank's required amount of capital and reserve funds in respect of gamma sensitivity, which gamma sensitivity measures the relevant rate of change in the delta value, and vega sensitivity, which vega sensitivity measures the sensitivity of the value of the option with respect to a change in volatility, which sensitivity parameters are associated with each relevant option position and shall be calculated in the manner approved or specified in writing by the Registrar, provided that— |
| (i) | in respect of the said calculation the bank shall treat the positions specified below as the same underlying: |
| (aa) | In the case of interest rates and in respect of each relevant maturity ladder per currency, each relevant time band specified in table 4 in paragraph (b), provided that a bank that adopted the duration method shall use the relevant time bands specified in table 6 in paragraph (b). |
| (bb) | In the case of equities and stock indices, each relevant national market sector. |
| (cc) | In the case of foreign currencies and gold, each relevant currency pair and gold. |
| (dd) | In the case of commodities, each relevant individual commodity. |
| (ii) | in respect of the relevant options relating to the same underlying the bank shall aggregate the relevant gamma impact value calculated in respect of each relevant option, which value may be either positive or negative, in order to determine a net gamma impact for each relevant underlying, which net gamma impact may be either positive or negative, provided that in the calculation of the bank's required amount of capital and reserve funds— |
| (aa) | the bank shall include only negative net gamma impacts; |
| (bb) | the total gamma capital requirement shall be equal to the sum of the absolute value of the net negative gamma impacts calculated in accordance with the relevant requirements specified in this subparagraph (iii); |
| (iii) | in respect of volatility risk the bank shall calculate its required amount of capital and reserve funds by firstly multiplying the sum of the relevant vega values for all options relating to the same underlying by a proportional shift in volatility of ± 25 per cent and then by aggregating the absolute value of the said individual capital requirements calculated for vega risk; |
| (C) | shall separately calculate the bank's capital requirements in respect of specific risk by multiplying the relevant delta-equivalent amount of each relevant option position with the relevant specific risk weights specified in paragraphs (b) and (c) above; |
| (D) | shall in the case of a delta-weighted position with a debt security or interest rate instrument as the underlying instrument include the said position in the relevant interest rate time band specified in paragraph (b) above in a manner similar to other derivative instruments, that is, based on a two legged approach, provided that the bank shall treat any floating rate instruments with caps or floors as a combination of floating rate instruments and a series of European-style options. |
For example—
| (i) | in respect of the reporting month of April, based on the relevant delta-equivalent value, the bank shall report a bought call option on a June three-month interest-rate future as a long position with a maturity of five months and a short position with a maturity of two months, and a written option as a long position with a maturity of two months and a short position with a maturity of five months; |
| (ii) | in respect of the reporting month of April, based on the relevant delta-equivalent value, the bank shall report a two months call option on a bond future in respect of which delivery of the bond takes place in September as a long position in respect of the bond and short a five months deposit; |
| (iii) | when the bank holds a three-year floating rate bond indexed to six month JIBAR with a cap of 15 per cent, the bank shall report a debt security that reprices in six months' time and a series of five written call options on a FRA with a reference rate of 15 per cent, each with a negative sign at the time the underlying FRA takes effect and a positive sign at the time the underlying FRA matures. |
| (E) | shall in the case of an option with an equity instrument as the underlying instrument, based on the relevant delta-weighted position, include the relevant position in the bank's measurement framework in accordance with the relevant requirements specified in paragraph (c) above, provided that the bank shall treat each relevant national market as a separate underlying; |
| (F) | shall in the case of an option in respect of a foreign exchange or gold position, based on the relevant delta equivalent of the said foreign currency or gold option, include the said position in the measurement of the bank's exposure in respect of the relevant currency or gold position in accordance with the relevant requirements specified in paragraph (d) above; |
| (G) | shall in the case of an option in respect of a commodity, based on the relevant requirements of the simplified or maturity ladder approach specified in paragraph (e) above, and the relevant delta-weighted position, include the said option position; |
| (H) | shall in respect of each relevant option position separately calculate the gamma impact according to a Taylor series expansion as: |
gamma impact = ½ x gamma x VU2
where:
| VU | is the variation in the price of the relevant underlying instrument of the option, which VU value— |
| (i) | shall in the case of an interest rate option in respect of which the underlying instrument is a bond be calculated by multiplying the market value of the said underlying instrument with the relevant risk weight specified in table 4 in paragraph (b), provided that the bank shall do a similar calculation when the underlying is an interest rate, in which case the bank's calculation shall be based on the relevant assumed change in the yield specified in table 4 in paragraph (b); |
| (ii) | shall in the case of an option in respect of an equity or equity index be calculated by multiplying the market value of the relevant underlying instrument with 8 per cent; |
| (iii) | shall in the case of an option in respect of foreign exchange or gold be calculated by multiplying the market value of the relevant underlying instrument with 8 per cent; |
| (iv) | shall in the case of an option in respect of a commodity be calculated by multiplying the market value of the said underlying instrument with 15 per cent. |
| (iv) | Matters relating to the scenario approach |
A bank that obtained the approval of the Registrar to adopt the scenario approach, which approach makes use of simulation techniques in order to calculate changes in the value of an options portfolio based on simultaneous changes in the relevant underlying rates or prices and the volatility of those rates or prices—
| (A) | shall separately calculate the bank's relevant capital requirements in respect of specific risk by multiplying the relevant delta-equivalent amount of each relevant option position with the relevant specific risk weights specified in paragraphs (b) and (c) above; |
| (B) | shall in order to calculate the bank's relevant required amount of capital and reserve funds in respect of general risk arising from all relevant option positions develop a scenario grid, that is, a matrix that contains a specified combination of underlying price and volatility changes, provided that— |
| (i) | based on the relevant requirements specified in the delta-plus approach, in subparagraph (iii)(B)(i) above, the bank— |
| (aa) | shall duly define the relevant underlying positions, provided that, subject to the prior written approval of and such conditions as may be specified in writing by the Registrar, a bank that conducts significant business in options may in respect of its interest rate options base the relevant required calculations on a minimum of six sets of time bands, provided that in no case shall the bank combine more than three of the relevant specified time bands; |
| (bb) | shall develop a separate matrix for each relevant individual underlying; |
| (ii) | in order to calculate the bank's relevant required amount of capital and reserve funds, the bank shall revalue the relevant option portfolio by making use of the said matrices for simultaneous changes in the option's underlying rate or price and the volatility of that rate or price; |
| (iii) | the bank shall evaluate the relevant options and the related hedging positions over the ranges specified in this sub-item (iii), |
| (aa) | which ranges are specified above and below the current value of the relevant underlying; |
| (bb) | which range shall in the case of interest rates be consistent with the assumed changes in yield specified in table 4 in paragraph (b), provided that a bank that obtained the approval of the Registrar to combine time bands in respect of interest rate options shall in respect of each relevant combined time band apply the highest of the assumed changes in yield applicable to the relevant group to which the time band belongs. |
For example, when the bank combines time bands 3 to 4 years, 4 to 5 years and 5 to 7 years the highest assumed change in yield of the said three bands shall be equal to 0.75.
| (cc) | which range shall in the case of equities be equal to ± 8 per cent; |
| (dd) | which range shall in the case of foreign exchange and gold be equal to ± 8 per cent; |
| (ee) | which range shall in the case of commodities be equal to ± 15 per cent, |
Provided that for each relevant risk category, in order to divide the relevant total range into equally spaced intervals, the bank shall use the number of observations specified in writing by the Registrar, which number of observations shall in no case be less than seven observations or price points and shall include the relevant current observation.
| (iv) | in respect of the second dimension of each relevant matrix the bank shall apply a single change in the volatility of the underlying rate or price equal to +25 per cent and -25 per cent, provided that the Registrar may require a bank— |
| (aa) | to apply a different change in volatility; and/or |
| (bb) | to calculate intermediate points on the relevant grid; |
| (v) | in respect of each relevant underlying the bank's capital requirement shall be equal to the largest loss contained in the relevant matrix, that is, after calculating the relevant amounts in respect of each relevant matrix each relevant cell in the matrix shall reflect the relevant net profit or loss of the option and the underlying hedge instrument, and the bank's capital requirement shall be equal to the largest loss contained in the relevant matrix; |
| (C) | shall in addition to the risks specified in this paragraph (f) duly monitor all other relevant risks arising from option positions, such as rho, that is, the rate of change in the value of an option with respect to the interest rate, and theta, that is, the rate of change in the value of the option with respect to time; |
| (D) | may in the calculation of the bank's minimum required amount of capital and reserve funds in respect of interest rate risk include rho. |
