2.7 THE STANDARDIZED MEASUREMENT METHOD
2.7.6 Treatment of Options .1 Segregation
2.7.5.3 Determination of Capital Requirements
The requirements to support commodities risk amount to 20 percent of the net position per commodities group. In order to take account of the base and time-structure risk, an additional capital charge of 3 percent of gross positions (sum of the absolute values of long and short positions) of all commodities groups is applied.
2.7.6 Treatment of Options
In the simplified approach, the positions for the options and the as- sociated underlying instrument, cash, or forward are not subject to the standardized methodology but rather are carved out and subject to sepa- rately calculated capital charges that incorporate both general market risk and specific risk. The risk numbers thus generated are then added to the capital charges for the relevant category—that is, interest-rate-related in- struments, equities, foreign exchange, and commodities. 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 standardized methodology, with the delta-equivalent amount subject to the applicable general market risk charges. Separate capital charges are then applied to the gamma and vega risks of the option positions. The sce- nario approach uses simulation techniques to calculate changes in the value of an options portfolio for changes in the level and volatility of its associated underlying instruments. Under this approach, the general mar- ket risk charge is determined by the scenario grid (i.e., the specified com- bination of underlying and volatility changes) that produces the largest loss. For the delta-plus method and the scenario approach, the specific risk capital charges are determined separately by multiplying the delta equiv- alent of each option by the specific risk weights.
Three approaches are admissible for the computation of capital re- quirements on option positions: the simplified procedure for institutions that use only purchased options, the delta-plus method, and scenario analysis for all other institutions.
Simplified Approach
In the case of the simplified approach, options are not to be included under the standard approach in regard to specific risk and general market risk, but they are subject to capital requirements computed separately. The risk values so computed are then added to the capital requirements for the individual categories—that is, interest-rate instruments, equities, foreign exchange, gold, and commodities.
• Purchased call and put options. The capital requirements correspond to the smaller of:
The market value of the option
The market value of the underlying instrument (contract volume, i.e., market values of the underlying instruments) multiplied by the sum of the rates for general market risk and (if applicable) for specific market risk in relation to the underlying instrument.
• Long cash position and purchased put option or short cash position and purchased call option. The capital requirements correspond to the market value of the underlying instrument (contract volume, i.e.,
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market values of the underlying instruments) multiplied by the sum of the rates for general market risk and (if applicable) for specific risk in relation to the underlying instrument less the intrinsic value of the option. The total requirement, however, cannot be a negative value. The corresponding underlying instruments are no longer to be included in the standard method.
(See Table 2-10.)
Intermediate Approach: Delta-Plus Method
Banks that write options are allowed to include delta-weighted options positions within the standardized methodology. If options are dealt with in accordance with the delta-plus method, they are to be mapped as posi- tions that correspond to the market value of the underlying instrument (contract volume, i.e., market values of the underlying instruments) mul- tiplied by the delta (sensitivity of the option price in relation to changes in the price of the underlying instrument). Depending on the underlying in- strument, they are included in the computation of capital requirements for specific and general market risk. As the risks of options are, however, in- adequately captured by the delta, institutions must also measure the
T A B L E 2-10
Simplified Approach: Capital Charges
Position Treatment
Long cash and long put The capital charge is the market value of the Short cash and long call underlying security* multiplied by the sum of specific and general market risk charges†for the underlying security less the amount the option is in the money (if any) bounded at zero.‡ Long call or long put The capital charge is the lesser of:
The market value of the underlying security multiplied by the sum of specific and general market risk charges for the underlying security The market value of the option
*In some cases, such as foreign exchange, 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—caps and floors, swaptions, etc.
†Some options (e.g., where the underlying security 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 (e.g., options on a corporate debt security or corporate bond index) and for options on equities and stock indexes. The charge under this measure for currency options will be 8 percent and for options on commodities 15 percent.
‡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.
¶Where the position does not fall within the trading book (i.e., options on certain foreign-exchange or commodities positions not belonging to the trading book), it may be acceptable to use the book value instead.
gamma risk (risk resulting from nonlinear relationships between option price changes and changes in the underlying instrument) and vega risk (risk resulting from the sensitivity of the option price to fluctuations of volatility of the underlying instrument).
• Delta risk. Capital requirements for delta risk on options with interest-rate instruments, equities, foreign exchange, and commodities are based on the delta-weighted positions.
In computing the general market risk, delta-weighted options on debentures or interest rates are allocated to the time bands for interest-rate instruments and (if applicable) also for computing specific risk. Options on derivatives are to be mapped twice, like the corresponding derivatives themselves. Thus, an April purchase of a June call option on a three-month interest-rate future—on the basis of its delta equivalent—will be consid- ered as a long position with a maturity of five months and as a short posi- tion with a maturity of two months. The written option will similarly be entered as a long position with a maturity of two months and a short po- sition with a maturity of five months.
Options on equities, foreign exchange, gold, and commodities will also be incorporated into the measurement values as delta-weighted positions.
• Gamma risk. For each individual option, a gamma effect, as defined here, is to be computed:
Gamma effect =0.5 ⋅ γ ⋅ δ2 (2.10) where γdesignates gamma and δthe change in the underlying value of the option. δis computed by multiplying the market value of the (notional) underlying value (contract volume, i.e., amount receivable of the underlying value or nominal value) by the following factors:
Interest-rate options: risk weight in accordance with Table 2-4 [dependent on the maturity of the (notional) underlying instrument]
Options on equities or stock indexes: 8 percent Options on foreign exchange or gold: 10 percent Options on commodities: 20 percent
A net gamma effect is to be computed from the gamma effects for the same categories of underlying instruments. The individual categories are defined as follows:
• Interest-rate instruments of the same currency and the same time band
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• Equities and stock indexes of the same national market or the same currency zone
• Foreign currencies of each identical currency pair
• Gold
• Commodities
Only the negative net gamma effects are to be included in the com- putation of required equity and to be summed as absolute values to arrive at the total capital requirement.
The method of computing the gamma capital requirements pre- sented here takes into account only general market risk. Banks that pos- sess significant positions in options on specific equities or debt instruments must, however, take specific risks into consideration in com- puting gamma effects.
• Vega risk. For each individual option, a vega effect, as defined here, is to be computed:
Vega effect =0.25 ⋅ ν ⋅volatility (2.11) where νdesignates the value of vega.
For each category of underlying instruments, a net vega effect is to be computed by addition of all vega effects of long positions (purchased options) and subtraction of all vega effects of short positions (sold op- tions). The total capital requirements for the vega risk subject to a capital charge result from the aggregation of the sum of absolute values of net vega effects computed for each category.
The computation of vega effects is to be made based on implicit volatilities. In the case of illiquid underlying instruments, other methods may be used on an exception basis to determine the volatility structure.
Intermediate Approach: Scenario Method
More sophisticated banks also have the right to base the market risk capi- tal charge for options portfolios and associated hedging positions on sce- nario matrix analysis. This is 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 charge, the bank revalues the option portfolio using matrices for simultaneous changes in the option’s under- lying rate or price and in the volatility of that rate or price. A different ma- trix is set up for each individual underlying instrument, as previously defined. As an alternative, at the discretion of each national authority, banks that are significant traders in options are permitted to base the cal- culation for interest-rate options on a minimum of six sets of time bands.
When using this method, no more than three time bands should be com- bined into any one set.
In computing the capital requirements for options and related hedging positions using scenario analysis, the potential change in value for all possi- ble combinations of changes in the underlying instrument or rate (dimension 1) and volatility (dimension 2), within the framework of a separate standard matrix, is to be computed for each category of underlying instruments or rates.94In the case of interest-rate instruments, it is possible to carry out a sep- arate analysis not for the instruments of each time band but to summarize the time bands into groups. However, a maximum of three time bands may grouped together, and at least six different groups must be formed. For foreign-exchange options in the scenario definition, the arbitrage relation- ship between the underlying instruments may be taken into consideration.
In such cases, the scenarios can be defined uniformly against the U.S. dollar.
The dimensions of the matrices to be used are defined as follows:
• Change in value of underlying instrument or rate (dimension 1). The computations are to be made within the range for at least seven different changes in value (including a change of 0 percent), where the assumed changes in value are at equally spaced intervals. The ranges are to be defined as follows:
Interest-rate options: Plus or minus the change in yield, in accordance with Table 2-6. Should several time bands be regrouped, the highest of the rates of the regrouped time bands shall apply for the group.
Options on equities and stock indexes: ⫾8 percent.
Options on foreign exchange and gold: ⫾10 percent.
Options on commodities: ⫾20 percent.
Computations on the basis of these value changes take into account only general market risk, not specific risk. The requirement for specific risk is thus to be computed separately, based on the delta- weighted positions (cf. secs. 1.2 and 1.3 of the 1996 amendment).
• Change in volatility (dimension 2). In regard to the variation in volatility, computations are to be conducted for at least three points: an unchanged volatility as well as relative changes in volatility of ⫾25 percent each.
After the computation of the matrix, each cell contains the net gain or loss of options and related hedging positions. The capital requirement computed for each category of underlying instrument corresponds in this case to the greatest of the losses contained in the matrix.
The scenario analysis is to be made based upon implicit volatilities.
In the case of illiquid underlying instruments, other methods may be used on an exception basis to determine the volatility structure.
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