Treatment of Options

No: 44047144

Date(g): 27/12/2022 | Date(h): 4/6/1444

Status: In-Force

14.74	In recognition of the wide diversity of banks’ activities in options and the difficulties of measuring price risk for options, two alternative approaches will be permissible at the discretion of SAMA under the simplified standardised approach.
	(1)	Those banks which solely use purchased options⁸¹ can use the simplified approach described in [14.76] below];
	(2)	Those banks which also write options are expected to use the delta-plus method or scenario approach which are the intermediate approaches as set out in [14.77] to [14.86]. The more significant its trading activity is, the more the bank will be expected to use a sophisticated approach, and a bank with highly significant trading activity is expected to use the standardised approach or the internal models approach as set out in [6] to [9] or [10] to [13].
14.75	In the simplified approach for options, the positions for the options and the associated underlying, cash or forward, are not subject to the standardised methodology but rather are carved-out and subject to separately calculated capital requirements that incorporate both general market risk and specific risk. The risk numbers thus generated are then added to the capital requirements for the relevant category, ie interest rate related instruments, equities, FX and commodities as described in [14.3] to [14.73]. The delta-plus method uses the sensitivity parameters or Greek letters associated with options to measure their market risk and capital requirements. Under this method, the delta-equivalent position of each option becomes part of the simplified standardised approach set out in [14.3] to [14.73] with the delta- equivalent amount subject to the applicable general market risk charges. Separate capital requirements are then applied to the gamma and vega risks of the option positions. The scenario approach uses simulation techniques to calculate changes in the value of an options portfolio for changes in the level and volatility of its associated underlyings. Under this approach, the general market risk charge is determined by the scenario grid (ie the specified combination of underlying and volatility changes) that produces the largest loss. For the delta-plus method and the scenario approach, the specific risk capital requirements are determined separately by multiplying the delta-equivalent of each option by the specific risk weights set out in [14.3] to [14.52].

Simplified approach

14.76

Banks that handle a limited range of purchased options can use the simplified approach set out in Table 11 for particular trades. As an example of how the calculation would work, if a holder of 100 shares currently valued at USD 10 each holds an equivalent put option with a strike price of USD 11, the capital requirement would be: USD 1,000 x 16% (ie 8% specific plus 8% general market risk) = USD 160, less the amount the option is in the money (USD 11 - USD 10) x 100 = USD 100, ie the capital requirement would be USD 60. A similar methodology applies for options whose underlying is a foreign currency, an interest rate related instrument or a commodity.

Simplified approach: capital requirements		Table 11
Position	Treatment
Long cash and long put or short cash and long call	The capital requirement will be the market value of the underlying security⁸² multiplied by the sum of specific and general market risk charges⁸³ for the underlying less the amount the option is in the money (if any) bounded at zero⁸⁴
Long call or long put	The capital requirement will be the lesser of: (i) the market value of the underlying security multiplied by the sum of specific and general market risk charges⁸² for the underlying and (ii) the market value of the option⁸⁵

Delta-plus method
14.77	Banks that write options will be allowed to include delta-weighted options positions within the simplified standardised approach set out in [14.3] to [14.73]. Such options should be reported as a position equal to the market value of the underlying multiplied by the delta. However, since delta does not sufficiently cover the risks associated with options positions, banks will also be required to measure 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) sensitivities in order to calculate the total capital requirement. These sensitivities will be calculated according to an approved exchange model or to the bank’s proprietary options pricing model subject to oversight by SAMA.⁸⁶
14.78	Delta-weighted positions with debt securities or interest rates as the underlying will be slotted into the interest rate time bands, as set out in [14.3] to [14.40], under the following procedure. A two-legged approach should be used as for other derivatives, requiring one entry at the time the underlying contract takes effect and a second at the time the underlying contract matures. For instance, 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 five-month maturity and a short position with a two-month maturity.⁸⁷ The written option will be similarly slotted as a long position with a two-month maturity and a short position with a five-month maturity. Floating rate instruments with caps or floors will 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 month LIBOR with a cap of 15% will treat it as:
	(1)	a debt security that reprices in six months; and
	(2)	a series of five written call options on an FRA with a reference rate of 15%, each with a negative sign at the time the underlying FRA takes effect and a positive sign at the time the underlying FRA matures.⁸⁸
14.79	The capital requirement for options with equities as the underlying will also be based on the delta-weighted positions that will be incorporated in the measure of equity risk described in [14.41] to [14.52]. For purposes of this calculation each national market is to be treated as a separate underlying. The capital requirement for options on FX and gold positions will be based on the method for FX rate risk as set out in [14.53] to [14.62]. For delta risk, the net delta-based equivalent of the foreign currency and gold options will be incorporated into the measurement of the exposure for the respective currency (or gold) position. The capital requirement for options on commodities will be based on the simplified or the maturity ladder approach for commodities risk as set out in [14.63] to [14.73]. The delta-weighted positions will be incorporated in one of the measures described in that section.
14.80	In addition to the above capital requirements arising from delta risk, there are further capital requirements for gamma and vega risk. Banks using the delta-plus method will be required to calculate the gamma and vega for each option position (including hedge positions) separately. The capital requirements should be calculated in the following way:
	(1)	For each individual option a gamma impact should be calculated according to a Taylor series expansion as follows, where VU is the variation of the underlying of the option.

	(2)	VU is calculated as follows:
		(a)	For interest rate options if the underlying is a bond, the market value of the underlying should be multiplied by the risk weights set out in [14.26]. An equivalent calculation should be carried out where the underlying is an interest rate, again based on the assumed changes in the corresponding yield in [14.26].
		(b)	For options on equities and equity indices: the market value of the underlying should be multiplied by 8%.⁸⁹
		(c)	For FX and gold options: the market value of the underlying should be multiplied by 8%.
		(d)	For options on commodities: the market value of the underlying should be multiplied by 15%.
	(3)	For the purpose of this calculation the following positions should be treated as the same underlying:
		(a)	for interest rates,⁹⁰ each time band as set out in [paragraph 718(iv) / [14.26];⁹¹
		(b)	for equities and stock indices, each national market;
		(c)	for foreign currencies and gold, each currency pair and gold; and
		(d)	for commodities, each individual commodity as defined in [14.67].
	(4)	Each option on the same underlying will have a gamma impact that is either positive or negative. These individual gamma impacts will be summed, resulting in a net gamma impact for each underlying that is either positive or negative. Only those net gamma impacts that are negative will be included in the capital requirement calculation.
	(5)	The total gamma risk capital requirement will be the sum of the absolute value of the net negative gamma impacts as calculated above.
	(6)	For volatility risk, banks will be required to calculate the capital requirements by multiplying the sum of the vega risks for all options on the same underlying, as defined above, by a proportional shift in volatility of ± 25%.
	(7)	The total capital requirement for vega risk will be the sum of the absolute value of the individual capital requirements that have been calculated for vega risk.

Scenario approach
14.81	More sophisticated banks may opt to base the market risk capital requirement for options portfolios and associated hedging positions on scenario matrix analysis. This will be accomplished by specifying a fixed range of changes in the option portfolio’s risk factors and calculating changes in the value of the option portfolio at various points along this grid. For the purpose of calculating the capital requirement, the bank will revalue the option portfolio using matrices for simultaneous changes in the option’s underlying rate or price and in the volatility of that rate or price. A different matrix will be set up for each individual underlying as defined in [14.80] above. As an alternative, at the discretion of SAMA, banks that are significant traders in options will for interest rate options be permitted to base the calculation on a minimum of six sets of time bands. When using this method, not more than three of the time bands as defined in [14.26] and [14.29] should be combined into any one set.
14.82	The options and related hedging positions will be evaluated over a specified range above and below the current value of the underlying. The range for interest rates is consistent with the assumed changes in yield in [14.26]. Those banks using the alternative method for interest rate options set out in [14.81] above should use, for each set of time bands, the highest of the assumed changes in yield applicable to the group to which the time bands belong.⁹² The other ranges are ± 8% for equities,⁹³ ± 8% for FX and gold, and ± 15% for commodities. For all risk categories, at least seven observations (including the current observation) should be used to divide the range into equally spaced intervals.
14.83	The second dimension of the matrix entails a change in the volatility of the underlying rate or price. A single change in the volatility of the underlying rate or price equal to a shift in volatility of + 25% and - 25% is expected to be sufficient in most cases. As circumstances warrant, however, SAMA may choose to require that a different change in volatility be used and/or that intermediate points on the grid be calculated.
14.84	After calculating the matrix, each cell contains the net profit or loss of the option and the underlying hedge instrument. The capital requirement for each underlying will then be calculated as the largest loss contained in the matrix.
14.85	The application of the scenario analysis by any specific bank will be subject to SAMA consent, particularly as regards the precise way that the analysis is constructed. Banks’ use of scenario analysis as part of the simplified standardised approach will also be subject to validation by SAMA, and to those of the qualitative standards for internal models as set out in [10].
14.86	Besides the options risks mentioned above, SAMA is conscious of the other risks also associated with options, eg rho (rate of change of the value of the option with respect to the interest rate) and theta (rate of change of the value of the option with respect to time). While not proposing a measurement system for those risks at present, it expects banks undertaking significant options business at the very least to monitor such risks closely. Additionally, banks will be permitted to incorporate rho into their capital calculations for interest rate risk, if they wish to do so.

⁸¹ Unless all their written option positions are hedged by perfectly matched long positions in exactly the same options, in which case no capital requirement for market risk is required.
⁸² In some cases such as FX, it may be unclear which side is the underlying security; this should be taken to be the asset that would be received if the option were exercised. In addition, the nominal value should be used for items where the market value of the underlying instrument could be zero, eg caps and floors, swaptions etc.
⁸³ Some options (eg where the underlying is an interest rate, a currency or a commodity) bear no specific risk but specific risk will be present in the case of options on certain interest rate related instruments (eg options on a corporate debt security or corporate bond index; see [14.3] to [14.40] for the relevant capital requirements) and for options on equities and stock indices (see [14.41] to [14.52]). The charge under this measure for currency options will be 8% and for options on commodities 15%.
⁸⁴ For options with a residual maturity of more than six months, the strike price should be compared with the forward, not current, price. A bank unable to do this must take the in the money amount to be zero.
⁸⁵ Where the position does not fall within the trading book (ie options on certain FX or commodities positions not belonging to the trading book), it may be acceptable to use the book value instead.
⁸⁶ SAMA may wish to require banks doing business in certain classes of exotic options (eg barriers, digitals) or in options at the money that are close to expiry to use either the scenario approach or the internal models alternative, both of which can accommodate more detailed revaluation approaches.
⁸⁷ A two-month call option on a bond future where delivery of the bond takes place in September would be considered in April as being long the bond and short a five-month deposit, both positions being delta-weighted.
⁸⁸ The rules applying to closely matched positions set out in [14.36] will also apply in this respect.
⁸⁹ The basic rules set out here for interest rate and equity options do not attempt to capture specific risk when calculating gamma capital requirements. Hoever, SAMA may wish to require specific banks to do so.
⁹⁰ Positions have to be slotted into separate maturity ladders by currency.
⁹¹ Banks using the duration method should use the time bands as set out in [14.29].
⁹² If, for example, the time bands 3 to 4 years, 4 to 5 years and 5 to 7 years are combined the highest assumed change in yield of these three bands would be 0.75.
⁹³ The basic rules set out here for interest rate and equity options do not attempt to capture specific risk when calculating gamma capital requirements. However, SAMA may wish to require specific banks to do so.