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  • CA-8 CA-8 Options risk - Standardised approach

    • CA-8.1 CA-8.1 Introduction

      • CA-8.1.1

        It is recognised that the measurement of the price risk of options is inherently a difficult task, which is further complicated by the wide diversity of banks' activities in options. The Central Bank has decided that the following approaches should be adopted to the measurement of options risks:

        (a) Banks which solely use purchased options are permitted to use the simplified (carve-out) approach described later in this Chapter.
        (b) Banks which also write options should use either the delta-plus (buffer) approach or the scenario approach, or alternatively use a comprehensive risk management model. The Central Bank's detailed rules for the recognition and use of internal models are included in Chapter CA-9.
        October 07

      • CA-8.1.2

        The scenario approach and the internal models approach are generally regarded as more satisfactory for managing and measuring options risk, as they assess risk over a range of outcomes rather than focusing on the point estimate of the 'Greek' risk parameters as in the delta-plus approach. The more significant the level and/or complexity of the bank's options trading activities, the more the bank will be expected to use a sophisticated approach to the measurement of options risks. The Central Bank will monitor the banks' options trading activities, and the adequacy of the risk measurement framework adopted.

        October 07

      • CA-8.1.3

        Where written option positions are hedged by perfectly matched long positions in exactly the same options, no capital charge for market risk is required in respect of those matched positions.

        October 07

    • CA-8.2 CA-8.2 Simplified approach (carve-out)

      • CA-8.2.1

        In the simplified approach, positions for the options and the associated underlying (hedges), cash or forward, are entirely omitted from the calculation of capital charges by the standardised methodology and are, instead, 'carved out' and subject to separately calculated capital charges that incorporate both general market risk and specific risk. The capital charges thus generated are then added to the capital charges for the relevant risk Category, i.e., interest rate related instruments, equities, foreign exchange and commodities as described in Chapters CA-4, CA-5, CA-6 and CA-7 respectively.

        October 07

      • CA-8.2.2

        The capital charges for the carved out positions are as set out in the table below. As an example of how the calculation would work, if a bank holds 100 shares currently valued at $ 10 each, and also holds an equivalent put option with a strike price of $ 11, the capital charge would be as follows:

        [$ 1,000 × 16%12] minus [($ 11 - $ 10)13 × 100] = $ 60

        A similar methodology applies to options whose underlying is a foreign currency, an interest rate related instrument or a commodity.

        128% specific risk plus 8% general market risk.

        13 The amount the option is 'in the money'.

        Simplified approach: Capital charges

        Position Treatment
        Long cash and long put

        or

        Short cash and long call (i.e. hedged positions)                 		The capital charge is:

        [Market value of underlying instrument14 x Sum of specific and general market risk charges15 for the underlying] minus [Amount, if any, the option is in the money16]

        The capital charge calculated as above is bounded at zero, i.e., it cannot be a negative number.
        Long call

        or

        Long put (i.e. naked option positions)         		The capital charge is the lesser of:

        i) Market value of the underlying instrument x Sum of specific and general market risk charges for the underlying; and

        ii) Market value of the option17.

        14 In some cases such as foreign exchange, it may be unclear which side is the 'underlying instrument'; this should be taken to be the asset which 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, e.g., caps and floors, swaptions etc.

        15 Some options (e.g., where the underlying is an interest rate, a currency or a commodity) bear no specific risk, but specific risk is present in the case of options on certain interest rate related instruments (e.g., options on a corporate debt security or a corporate bond index - see Chapter CA-4 for the relevant capital charges), and in the case of options on equities and stock indices (see Chapter CA-5 for the relevant capital charges). The capital charge for currency options is 8% and for options on commodities is 15%.

        16 For options with a residual maturity of more than six months, the strike price should be compared with the forward, not the current, price. A bank unable to do this should take the 'in the money' amount to be zero.

        17 Where the position does not fall within the trading book options on certain foreign exchange and commodities positions not belonging to the trading book), it is acceptable to use the book value instead of the market value.

        October 07

    • CA-8.3 CA-8.3 Delta-plus method (buffer approach)

      • CA-8.3.1

        Banks which write options are allowed to include delta-weighted option positions within the standardised methodology set out in Chapters CA-4 through CA-7. Each option should be reported as a position equal to the market value of the underlying multiplied by the delta. The delta should be calculated by an adequate model with appropriate documentation of the process and controls, to enable the Central Bank to review such models, if considered necessary. A worked example of the delta-plus method is set out in Appendix CA-6.

        October 07

      • CA-8.3.2

        Since delta does not sufficiently cover the risks associated with options positions, there will be additional capital buffers to cover 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), in order to calculate the total capital charge. The gamma and vega buffers should be calculated by an adequate exchange model or the bank's proprietary options pricing model, with appropriate documentation of the process and controls, to enable the Central Bank to review such models, if considered necessary.

        October 07

      • Treatment of delta

        • CA-8.3.3

          The treatment of the delta-weighted positions, for the calculation of the capital charges arising from delta risk, is summarised in Paragraphs CA-8.3.4 to CA-8.3.9.

          October 07

      • Where the underlying is a debt security or an interest rate

        • CA-8.3.4

          The delta-weighted option positions are slotted into the interest rate time-bands as set out in Chapter CA-4. A two-legged approach should be used as for other derivatives, as explained in Chapter CA-4, requiring one entry at the time the underlying contract takes effect and a second at the time the underlying contract matures. A few examples to elucidate the two-legged treatment are set out below:

          (a) 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 maturity of five months and a short position with a maturity of two months.
          (b) A written option with the same underlying as in (a) above, will be included in the measurement framework as a long position with a maturity of two months and a short position with a maturity of five months.
          (c) A two months call option on a bond future where delivery of the bond takes place in September will be considered in April, as being long the bond and short a five months deposit, both positions being delta-weighted.
          October 07

        • CA-8.3.5

          Floating rate instruments with caps or floors are 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 10% will treat it as:

          (a) A debt security that reprices in six months; and
          (b) A series of five written call options on an FRA with a reference rate of 10%, each with a negative sign at the time the underlying FRA takes effect and a positive sign at the time the underlying FRA matures.
          October 07

        • CA-8.3.6

          The rules applying to closely matched positions, set out in Paragraph CA-4.8.2, will also apply in this respect.

          October 07

      • Where the underlying is an equity instrument

        • CA-8.3.7

          The delta-weighted positions are incorporated in the measure of market risk described in Chapter CA-5. For purposes of this calculation, each national market is treated as a separate underlying.

          October 07

      • Options on foreign exchange and gold positions

        • CA-8.3.8

          The net delta-based equivalent of the foreign currency and gold options are incorporated in the measurement of the exposure for the respective currency or gold position, as described in Chapter CA-6.

          October 07

      • Options on commodities

        • CA-8.3.9

          The delta-weighted positions are incorporated in the measurement of the commodities risk by the simplified approach or the maturity ladder approach, as described in Chapter CA-7.

          October 07

      • Calculation of the gamma and vega buffers

        • CA-8.3.10

          As explained in Paragraph CA-8.3.2, in addition to the above capital charges to cover delta risk, banks are required to calculate additional capital charges to cover the gamma and vega risks. The additional capital charges are calculated as follows:

          •   Gamma
          (a) For each individual option position (including hedge positions), a gamma impact is calculated according to the following formula derived from the Taylor series expansion:

          Gamma impact = 0.5 × Gamma × VU

          where VU = variation of the underlying of the option, calculated as in (b) below
          (b) VU is calculated as follows:
          (i) For interest rate options18, where the underlying is a bond, the market value of the underlying is multiplied by the risk weights set out in Section CA-4.4. An equivalent calculation is carried out where the underlying is an interest rate, based on the assumed changes in yield as set out in the table in Section CA-4.5;
          (ii) For options on equities and equity indices18, the market value of the underlying is multiplied by 8%;
          (iii) For foreign exchange and gold options, the market value of the underlying is multiplied by 8%;
          (iv) For commodities options, the market value of the underlying is multiplied by 15%.
          (c) For the purpose of the calculation of the gamma buffer, the following positions are treated as the same underlying:
          (i) For interest rates, each time-band as set out in the table in Section CA-4.4. Positions should be slotted into separate maturity ladders by currency. Banks using the duration method should use the time-bands as set out in the table in Section CA-4.5;
          (ii) For equities and stock indices, each individual national market;
          (iii) For foreign currencies and gold, each currency pair and gold; and
          (iv) For commodities, each individual commodity as defined in Section CA-7.2.
          (d) Each option on the same underlying will have a gamma impact that is either positive or negative. These individual gamma impacts are summed, resulting in a net gamma impact for each underlying that is either positive or negative. Only those net gamma impacts that are negative are included in the capital calculation.
          (e) The total gamma capital charge is the sum of the absolute value of the net negative gamma impacts calculated for each underlying as explained in (d) above.
          •   Vega
          (f) For volatility risk (vega), banks are required to calculate the capital charges by multiplying the sum of the vegas for all options on the same underlying, as defined above, by a proportional shift in volatility of ±25%.
          (g) The total vega capital charge is the sum of the absolute value of the individual vega capital charges calculated for each underlying.

          18 For interest rate and equity options, the present set of rules do not attempt to capture specific risk when calculating gamma capital charges. See Section CA-8.4 for an explanation of the Central Bank's views on this subject.

          October 07

        • CA-8.3.11

          The capital charges for delta, gamma and vega risks described in Paragraphs CA-8.3.1 through CA-8.3.10 are in addition to the specific risk capital charges which are determined separately by multiplying the delta-equivalent of each option position by the specific risk weights set out in Chapters CA-4 through CA-7.

          October 07

        • CA-8.3.12

          To summarise, capital requirements for, say OTC options, using the delta-plus method are as follows:

          (a) Counterparty risk capital charges (on purchased options only), calculated in accordance with the credit risk regulations; PLUS
          (b) Specific risk capital charges (calculated as explained in Paragraph CA-8.3.11); PLUS
          (c) Delta risk capital charges (calculated as explained in Paragraphs CA-8.3.3 through CA-8.3.9) PLUS
          (d) Gamma and vega capital buffers (calculated as explained in Paragraph CA-8.3.10).
          October 07

    • CA-8.4 CA-8.4 Scenario approach

      • CA-8.4.1

        As stated in Section CA-8.1, banks which have a significant level of options trading activities, or have complex options trading strategies, are expected to use more sophisticated methods for measuring and monitoring the options risks. Banks with the appropriate capability will be permitted, with the prior approval of the Central Bank, to base the market risk capital charge for options portfolios and associated hedging positions on scenario matrix analysis. Before giving its approval, the Central Bank will closely review the accuracy of the analysis that is constructed. Furthermore, like in the case of internal models, the banks' use of scenario analysis as part of the standardised methodology will also be subject to external validation, and to those of the qualitative standards listed in Chapter CA-9 which are appropriate given the nature of the business.

        October 07

      • CA-8.4.2

        The scenario matrix analysis involves 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' or 'matrix'. For the purpose of calculating the capital charge, 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 is set up for each individual underlying as defined in Section CA-8.3 above. As an alternative, in respect of interest rate options, banks which are significant traders in such options are permitted to base the calculation on a minimum of six sets of time-bands. When using this alternative method, not more than three of the time-bands as defined in Chapter CA-4 should be combined into any one set.

        October 07

      • CA-8.4.3

        The first dimension of the matrix involves a specified range of changes in the option's underlying rate or price. The Central Bank has set the range for each risk Category as follows:

        (a) Interest rate related instruments - The range for interest rates is consistent with the assumed changes in yield set out in Section CA-4.5. Those banks using the alternative method of grouping time-bands into sets, as explained in Paragraph CA-8.4.2, should use, for each set of time-bands, the highest of the assumed changes in yield applicable to the individual time-bands in that group. 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 which would be applicable to that set.
        (b) For equity instruments, the range is ±8%.
        (c) For foreign exchange and gold, the range is ±8%.
        (d) For commodities, the range is ±15%,

        For all risk categories, at least seven observations (including the current observation) should be used to divide the range into equally spaced intervals.

        October 07

      • CA-8.4.4

        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% is applied.

        October 07

      • CA-8.4.5

        The Central Bank will closely monitor the need to reset the parameters for the amounts by which the price of the underlying instrument and volatility must be shifted to form the rows and columns of the scenario matrix. For the time being, the parameters set, as above, only reflect general market risk (see Paragraphs CA-8.4.10 to CA-8.4.12).

        October 07

      • CA-8.4.6

        After calculating the matrix, each cell contains the net profit or loss of the option and the underlying hedge instrument. The general market risk capital charge for each underlying is then calculated as the largest loss contained in the matrix.

        October 07

      • CA-8.4.7

        In addition to the capital charge calculated as above, the specific risk capital charge is determined separately by multiplying the delta-equivalent of each option position by the specific risk weights set out in Chapters CA-4 through CA-7.

        October 07

      • CA-8.4.8

        To summarise, capital requirements for, say OTC options, using the scenario approach are as follows:

        (a) Counterparty risk capital charges (on purchased options only), calculated in accordance with the credit risk regulations; PLUS
        (b) Specific risk capital charges (calculated as explained in Paragraph CA-8.4.7); PLUS
        (c) Directional and volatility risk capital charges (i.e., the worst case loss from a given scenario matrix analysis).
        October 07

      • CA-8.4.9

        Banks doing business in certain classes of complex exotic options (e.g. barrier options involving discontinuities in deltas etc.), or in options at the money that are close to expiry, are required to use either the scenario approach or the internal models approach, both of which can accommodate more detailed revaluation approaches. The Central Bank expects the concerned banks to work with it closely to produce an agreed method, within the framework of these rules. If a bank uses scenario matrix analysis, it must be able to demonstrate that no substantially larger loss could fall between the nodes.

        October 07

      • CA-8.4.10

        In drawing up the delta-plus and the scenario approaches, the Central Bank's present set of rules do not attempt to capture specific risk other than the delta-related elements (which are captured as explained in Paragraphs CA-8.4.7 and CA-8.4.11). The Central Bank recognises that introduction of those other specific risk elements will make the measurement framework much more complex. On the other hand, the simplifying assumptions used in these rules will result in a relatively conservative treatment of certain options positions.

        October 07

      • CA-8.4.11

        In addition to the options risks described earlier in this Chapter, the Central Bank is conscious of the other risks also associated with options, e.g. rho or interest rate risk (the rate of change of the value of the option with respect to the interest rate) and theta (the rate of change of the value of the option with respect to time). While not proposing a measurement system for those risks at present, the Central Bank 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.

        October 07

      • CA-8.4.12

        The Central Bank will closely review the treatment of options for the calculation of market risk capital charges, particularly in the light of the aspects described in Paragraphs CA-8.4.10 and CA-8.4.11.

        October 07