BIPRU 7.6 Option PRR
Option PRR calculation
A firm must calculate its option PRR by:
 (1)
identifying which option positions must be included within the scope of the option PRR calculation under BIPRU 7.6.3R  BIPRU 7.6.5R;
 (2)
calculating the derived position in each option in accordance with BIPRU 7.6.9R  BIPRU 7.6.15R;
 (3)
calculating the PRR for each derived position in accordance with BIPRU 7.6.16R  BIPRU 7.6.31R;
 (4)
summing all of the PRRs calculated in accordance with (3).
Firms are reminded that the table in BIPRU 7.2.4R (Instruments which result in notional positions for the purposes of the interest rate PRR) and the table in BIPRU 7.3.3R (Instruments which result in notional positions for the purposes of the equity PRR) also require an interest rate PRR to be calculated for options on equities, baskets of equities or equities indices. The interaction between BIPRU 7.6 and the rest of Chapter 7 is illustrated in BIPRU 7.6.33G.
Scope of the option PRR calculation
Except as permitted under BIPRU 7.6.5R, a firm's option PRR calculation must include:
 (1)
each trading book position in an option on an equity, interest rate or debt security;
 (2)
each trading book position in a warrant on an equity or debt security;
 (3)
each trading book position in a CIU; and
 (4)
each trading book and nontrading book position in an option on a commodity, currency or gold.
Table: Appropriate PRR calculation for an option or warrant
This table belongs to BIPRU 7.6.3R
Option type (see BIPRU 7.6.18R) or warrant 
PRR calculation 
American option, European option, Bermudan option, Asian option or warrant for which the in the money percentage (see BIPRU 7.6.6R) is equal to or greater than the appropriate position risk adjustment (see BIPRU 7.6.7R and BIPRU 7.6.8R) 
Calculate either an option PRR, or the most appropriate to the underlying position of:

American option, European option, Bermudan option, Asian option or warrant:

Calculate an option PRR 
All other types of option listed in BIPRU 7.6.18R (regardless of whether in the money, at the money or out of the money). 
The in the money percentage
 (1)
The in the money percentage is calculated in accordance with this rule.
 (2)
For a call option:
Current market price of underlying  Strike price of the option * 100
Strike price of the option
 (3)
For a put option:
Strike price of option  Current market price of underlying * 100
Strike price of the option
 (4)
In the case of an option on a basket of securities a firm may not treat the option as being in the money by the relevant percentage so as to enable the firm not to apply an option PRR under BIPRU 7.6.5R unless the conditions in BIPRU 7.6.5R are satisfied with respect to each kind of underlying investment.
 (5)
(4) also applies to an option on a CIU if a firm is using one of the CIU look through methods.
The appropriate position risk adjustment
 (1)
The appropriate position risk adjustment for a position is that listed in the table in BIPRU 7.6.8R against the relevant underlying position.
 (2)
If the firm uses the commodity extended maturity ladder approach or the commodity maturity ladder approach for a particular commodity under BIPRU 7.4 (Commodity PRR) the appropriate position risk adjustment for an option on that commodity is the outright rate applicable to the underlying position (see BIPRU 7.4.26R (Calculating the PRR for each commodity: Maturity ladder approach) and BIPRU 7.4.33R (Table: Alternative spread, carry and outright rates)).
 (3)
If a firm does not have commodity positions treated under BIPRU 7.4 or does not have positions in the commodity in question treated under BIPRU 7.4 the restrictions in BIPRU 7.4 that regulate when a firm can and cannot use a particular method of calculating the commodity PRR apply for the purpose of establishing the appropriate position risk adjustment1 for the purposes of BIPRU 7.6.
 (4)
If a firm is using one of the CIU look through methods for an option on a CIU the leveraging requirements in BIPRU 7.7 (Position risk requirements for collective investment undertakings) apply (see BIPRU 7.7.11R). For this purpose the amount of the appropriate position risk adjustments under BIPRU 7.6.6R(5) is increased by the amount of that leveraging (expressed as a percentage) as calculated under BIPRU 7.7, subject to a maximum appropriate position risk adjustment of 32%.
Table: Appropriate position risk adjustment
This table belongs to BIPRU 7.6.7R
Underlying position 

The position risk adjustment applicable to the underlying equity or equity index in the table in BIPRU 7.3.30R (Simplified equity method) 

Interest rate 
The sum of the specific risk position risk adjustment (see BIPRU 7.2.43R to BIPRU 7.2.51G (Specific risk calculation)) and the general market risk position risk adjustment (as set out in BIPRU 7.2.57R (General market risk position risk adjustments)) applicable to the underlying position 
Debt securities 
The sum of the specific risk position risk adjustment (see BIPRU 7.2.43R to BIPRU 7.2.51G (Specific risk calculation)) and the general market risk position risk adjustment (as set out in the table in BIPRU 7.2.57R (General market risk position risk adjustments)) applicable to the underlying position 
18% (unless BIPRU 7.6.7R requires otherwise) 

Currency 
8% 
Gold 
8% 
32% (subject to BIPRU 7.6.6R and BIPRU 7.6.7R) 
Calculating derived positions
A firm must calculate the derived position specified in the table in BIPRU 7.6.13R for each position included in its option PRR calculation.
Netting positions
A firm may calculate a derived position for its net position in an option or a warrant, if the relevant options or warrants are identical or may be treated as identical under BIPRU 7.6.11R or BIPRU 7.6.12R.
A firm may treat options or warrants as identical if they have the same strike price, maturity (except for an interest rate cap or floor  see BIPRU 7.6.12R) and underlying.
Derived positions
Table: Derived positions
This table belongs to BIPRU 7.6.9R
Underlying 
Option (or warrant) 
Derived position 
Option (warrant) on a single equity or option on a future/forward on a single equity 
A notional position in the actual equity underlying the contract valued at the current market price of the equity. 

Option (warrant) on a basket of equities or option on a future/forward on a basket of equities 
A notional position in the actual equities underlying the contract valued at the current market price of the equities. 

Option (warrant) on an equity index or option on a future/forward on an equity index 
A notional position in the index underlying the contract valued at the current market price of the index. 

Interest rate 
A zero coupon zerospecificrisk security in the currency concerned with a maturity equal to the sum of the time to expiry of the contract and the length of the period on which the settlement amount of the contract is calculated valued at the notional amount of the contract. 

A zero coupon zerospecificrisk security in the currency concerned with a maturity equal to the length of the swap valued at the notional principal amount. 

Interest rate cap or floor 
A zero coupon zerospecificrisk security in the currency concerned with a maturity equal to the remaining period of the cap or floor valued at the notional amount of the contract. 

Debt securities 
Option (warrant) on a debt security or option on a future/forward on a debt security 
The underlying debt security with a maturity equal to the time to expiry of the option valued as the nominal amount underlying the contract at the current market price of the debt security. 
Option (warrant) on a basket of debt securities or option on a future/forward on a basket of debt securities 
A notional position in the actual debt securities underlying the contract valued at the current market price of the debt securities. 

Option (warrant) on an index of debt securities or option on a future/forward on an index of debt securities 
A notional position in the index underlying the contract valued at the current market price of the index. 

Option on a commodity or option on a future/forward on a commodity 
An amount equal to the tonnage, barrels or kilos underlying the option with (in the case of a future/forward on a commodity) a maturity equal to the expiry date of the forward or Futures contract underlying the option. In the case of an option on a commodity the maturity of the position falls into Band 1 in the table in BIPRU 7.4.28R (Table: Maturity bands for the maturity ladder approach). 

An amount equal to the tonnage, barrels or kilos underlying the option with a maturity equal to the length of the swap valued at the notional principal amount. 

(These provisions about CIUs are subject to BIPRU 7.6.35R) 
Option (warrant) on a single CIU or option on a future/forward on a single CIU 
A notional position in the actual CIU underlying the contract valued at the current market price of the CIU. 
Option (warrant) on a basket of CIUs or option on a future/forward on a basket of CIUs 
A notional position in the actual CIUs underlying the contract valued at the current market price of the CIUs. 

Gold 
An amount equal to the troy ounces underlying the option with (in the case of a future/forward on gold) a maturity equal to the expiry date of the forward or futures contract underlying the option. 

Currency 
Currency option 
The amount of the underlying currency that the firm will receive if the option is exercised converted at the spot rate into the currency that the firm will sell if the option is exercised. 
Combinations of options which can be treated as one option
A firm may treat (for the purpose of calculating an option PRR under BIPRU 7.6) an option strategy listed in the table in BIPRU 7.6.15R as the single position in a notional option specified against that strategy in the table in BIPRU 7.6.15R, if:
 (1)
each element of the strategy is transacted with the same counterparty;
 (2)
the strategy is documented as a single structure;
 (3)
the underlying for each part of the composite position (including any actual holding of the underlying) is the same under the PRR identical product netting rules;
 (4)
the netting achieved does not result overall in a greater degree of netting in the calculation of the market risk capital requirement than would be permitted under the other standard market risk PRR rules;
 (5)
each option in the structure has the same maturity and underlying; and
 (6)
the constituent parts of the structure form an indivisible single contract, so that neither party can unwind or default on one part of the structure without doing so for the contract as a whole;
except that (1) and (6) only apply to the extent possible with respect to any part of the composite position held by the firm that consists of an actual holding of the underlying.
Table: Option strategies
This table belongs to BIPRU 7.6.14R
Option strategy (and an example) 
Notional option (and rule it must be treated under) 
Bull Spread (e.g. buy 100 call and sell 101 call) 
One purchased option (treat under BIPRU 7.6.20R) 
Bear Spread (e.g. sell 100 put and buy 101 put) 
One written option (treat under BIPRU 7.6.21R) 
Synthetic Long Call (e.g. long underlying and buy 100 put) 
One purchased option (treat under BIPRU 7.6.20R or BIPRU 7.6.24R) 
Synthetic Short Call (e.g. short underlying and sell 100 put) 
One written option (treat under BIPRU 7.6.21R or BIPRU 7.6.24R) 
Synthetic Long Put (e.g. short underlying and buy 100 call) 
One purchased option (treat under BIPRU 7.6.20R or BIPRU 7.6.24R) 
Synthetic Short Put (e.g. buy underlying and sell 100 call) 
One written option (treat under BIPRU 7.6.21R or BIPRU 7.6.24R) 
Long Straddle (e.g. buy 100 call and buy 100 put) 
One purchased option (treat under BIPRU 7.6.20R) 
Short Straddle (e.g. sell 100 call and sell 100 put) 
One written option (treat under BIPRU 7.6.21R but with no reduction for the amount the option is out of the money) 
Long Strangle (e.g. buy 101 call and buy 99 put) 
One purchased option (treat under BIPRU 7.6.20R) 
Short Strangle (e.g. sell 99 call and sell 101 put) 
One written option (treat under BIPRU 7.6.21R but with no reduction for the amount the option is out of the money) 
Long Butterfly (e.g. buy one 100 call, sell two 101 calls, and buy one 102 call) 
One purchased option (treat under BIPRU 7.6.20R) 
Short Butterfly (e.g. sell one 100 put, buy two 101 puts, and sell one 102 put) 
One written option (treat under BIPRU 7.6.21R but with no reduction for the amount the option is out of the money) 
The option PRR for an individual positions
A firm must calculate the option PRR for each individual derived option position using the method specified in the table in BIPRU 7.6.18R, or, if more than one method is permitted, using one of those methods.
A firm must convert its positions into its base currency in accordance with the procedures that apply for whichever of the other PRR charges is appropriate (see BIPRU 7.2.1R(3), BIPRU 7.3.1R(2), BIPRU 7.4.1R(3), BIPRU 7.5.19R(2), BIPRU 7.5.20R(3) and BIPRU 7.7.1R(3)).
Table: Option PRR: methods for different types of option
This table belongs to BIPRU 7.6.16R
Option 
Description 
Method 
American option 
An option that may be exercised at any time over an extended period up to its expiry date. 
Option standard method or option hedging method if appropriate 
European option 
An option that can only be exercised at expiry. 

Bermudan option 
A cross between an American option and European option. The Bermudan option can only be exercised at specific dates during its life. 

Asian option 
The buyer has the right to exercise at the average rate or price of the underlying over the period (or part of the period) of the option. One variant is where the payout is based on the average of the underlying against a fixed strike price; another variant is where the payout gives at expiry the price of the underlying against the average price over the option period. 
Option standard method or option hedging method if appropriate 
Barrier option 
An option which is either cancelled or activated if the price of the underlying reaches a preset level regardless of the price at which the underlying may be trading at the expiry of the option. The knockout type is cancelled if the underlying price or rate trades through the trigger; while the knockin becomes activated if the price moves through the trigger. 

Corridor option 
Provides the holder with a payout for each day that the underlying stays within a defined range chosen by the investor. 

Ladder option 
Provides the holder with guaranteed payouts if the underlying trades through a preagreed price(s) or rate(s) at a certain point(s) in time, regardless of future performance. 

Lockin option 
An option where the payout to the holder is locked in at the maximum (or minimum) value of the underlying that occurred during the life of the option. 

Lookback option 
A European style option where the strike price is fixed in retrospect, that is at the most favourable price (i.e. the lowest (highest) price of the underlying in the case of a call (put)) during the life of the option. 

Forward starting option 
An option that starts at a future date. 

Compound option 
An option where the underlying is itself an option (i.e. an option on an option). 
Option standard method or option hedging method if appropriate 
Interest rate cap 
An interest rate option or series of options under which a counterparty contracts to pay any interest costs arising as a result of an increase in rates above an agreed rate: the effect being to provide protection to the holder against a rise above that agreed interest rate. 
Option standard method, but no reduction for the amount the option is out of the money is permitted 
Interest rate floor 
An interest rate option or series of options under which a counterparty contracts to pay any lost income arising as a result of a fall in rates below an agreed rate: the effect being to provide protection to the holder against a fall below that agreed interest rate. 

Performance option 
An option based on a reference basket comprising any number of assets, where the payout to the holder could be one of the following: the maximum of the worst performing asset, or 0; the maximum of the best performing asset, or 0; the maximum of the spreads between several pairs of the assets, or 0. 
Option standard method or option hedging method  using the highest position risk adjustment of the individual assets in the basket 
Quanto 
Quanto stands for "Quantity Adjusted Option". A quanto is an instrument where two currencies are involved. The payoff is dependent on a variable that is measured in one of the currencies and the payoff is made in the other currency. 
Subject to BIPRU 7.6.31R, the option standard method 
Cliquet option 
A cliquet option consists of a series of forward starting options where the strike price for the next exercise date is set equal to a positive constant times the underlying price as of the previous exercise date. It initially acts like a vanilla option with a fixed price but as time moves on, the strike is reset and the intrinsic value automatically locked in at preset dates. If the underlying price is below the previous level at the reset date no intrinsic value is locked in but the strike price will be reset to the current price attained by the underlying. If the underlying price exceeds the current level at the next reset the intrinsic value will again be locked in. 
Option standard method for a purchased cliquet, or the method specified in BIPRU 7.6.30R for a written cliquet 
Digital option 
A type of option where the payout to the holder is fixed. The most common types are allornothing and onetouch options. Allornothing will pay out the fixed amount if the underlying is above (call) or below (put) a set value at expiry. The onetouch will pay the fixed amount if the underlying reaches a fixed point any time before expiry. 
The method specified in BIPRU 7.6.29 R 
The method specified for the type of instrument whose description it most closely resembles. 
 (1)
The option standard method is described in BIPRU 7.6.20R  BIPRU 7.6.22R.
 (2)
The option hedging method is described in BIPRU 7.6.23G  BIPRU 7.6.28R.
The standard method: Purchased options and warrants
Under the option standard method, the PRR for a purchased option or warrant is the lesser of:
 (1)
the market value of the derived position (see BIPRU 7.6.9R) multiplied by the appropriate position risk adjustment (see BIPRU 7.6.8R); and
 (2)
The standard method: Written options and warrants
Under the option standard method, the PRR for a written option or warrant is the market value of the derived position (see BIPRU 7.6.9R) multiplied by the appropriate position risk adjustment (see BIPRU 7.6.8R). This result may be reduced by the amount the option or warrant is out of the money (subject to a maximum reduction to zero).
The standard method: Underwriting or subunderwriting an issue of warrants
Under the option standard method, the PRR for underwriting or subunderwriting an issue of warrants is the net underwriting position (or reduced net underwriting position) multiplied by the current market price of the underlying securities multiplied by the appropriate position risk adjustment, but the result can be limited to the value of the net underwriting position (or reduced net underwriting position) calculated using the issue price of the warrant.
The hedging method
The option hedging method involves the option PRR being calculated on a combination of the option and its hedge.
Under the option hedging method a firm must calculate the option PRR for individual positions as follows:
 (1)
for an option or warrant on an equity, basket of equities or equity index and its equity hedge(s), the firm must, to the extent specified or permitted in the table in BIPRU 7.6.26R, use the calculation in the table in BIPRU 7.6.27R;
 (2)
for an option or warrant on a debt security, basket of debt securities or debt security index and its debt security hedge(s), the firm must, to the extent specified or permitted in the table in BIPRU 7.6.26R, use the calculation in the table in BIPRU 7.6.27R;
 (3)
for an option on gold and its gold hedge, the firm must, to the extent specified or permitted in the table in BIPRU 7.6.26R, use the calculation in the table in BIPRU 7.6.27R; and
 (4)
for an option on a currency and its currency hedge, the firm must, to the extent specified or permitted in the table in BIPRU 7.6.26R, use the calculation in the table in BIPRU 7.6.28R.
 (1)
A firm may not use the option hedging method for:
 (a)
an interest rate option and its hedge; or
 (b)
a commodity option and its hedge; or
 (c)
 (a)
 (2)
A firm may only use the option hedging method if the item underlying the option or warrant is the same as the hedge of the option or warrant under the PRR identical product netting rules.
Table: Appropriate treatment for equities, debt securities or currencies hedging options
This table belongs to BIPRU 7.6.24R
Hedge 
PRR calculation for the hedge 
Limits (if hedging method is used) 
Naked position 
The equity must be treated in either BIPRU 7.3 (equity PRR) or the option hedging method (see the table in BIPRU 7.6.27R) 
The option hedging method must only be used up to the amount of the hedge that matches the notional amount underlying the option or warrant 
To the extent that the amount of the hedge (or option or warrant) exceeds the notional amount underlying the option or warrant (or hedge), a firm must apply an equity PRR, interest rate PRR or foreign currency PRR (or the option standard method) 

The debt security must be treated in BIPRU 7.2 (interest rate PRR) or the option hedging method (see the table in BIPRU 7.6.27R) 
As for the first row 
As for the first row 

Gold (hedging a gold option) 
The gold must be treated in either BIPRU 7.5 (Foreign currency PRR) or the option hedging method (see the table in BIPRU 7.6.27R) 
As for the first row 
As for the first row 
A currency or currencies (hedging a currency option) 
The currency must be treated in either BIPRU 7.5 (Foreign currency PRR) or the option hedging method (see the table in BIPRU 7.6.28R) 
As for the first row 
As for the first row 
Table: The hedging method of calculating the PRR (equities, debt securities and gold)
This table belongs to BIPRU 7.6.24R(1)  (3)
PRR 

In the money by more than the position risk adjustment 
In the money by less than the position risk adjustment 

Long in security or gold 
Long put 
Zero 
Wp 
X 
Short call 
Y 
Y 
Z 

Short in security or gold 
Long call 
Zero 
Wc 
X 
Short put 
Y 
Y 
Z 

Where: 

Wp means 
{(position risk adjustment100%) x The underlying position valued at strike price} 
+ 
The market value of the underlying position 

Wc means 
{(100% +position risk adjustment x The underlying position valued at strike price} 
 
The market value of the underlying position 

X means 
The market value of the underlying position multiplied by the appropriate position risk adjustment 

Y means 
The market value of the underlying position multiplied by the appropriate position risk adjustment. This result may be reduced by the market value of the option or warrant, subject to a maximum reduction to zero. 

Z means 
The option hedging method is not permitted; the option standard method must be used. 
Table: The hedging method of calculating the PRR (currencies)
This table belongs to BIPRU 7.6.24R(4)
In the money by more than 8% 
In the money by less than 8% 

Long calls & long puts 
Zero 
W_{L} 
X 
Short calls & short puts 
Zero 
Y 
X 
Where: 

W_{L} means 
(1.08% x U) 
 
The market value of the underlying position 
U means 
The amount of the underlying currency that the firm will receive if the option is exercised, converted at the strike price into the currency that the firm will sell if the option is exercised 

X means 
The market value of the underlying position multiplied by 8%. 

Y means 
The market value of the underlying position multiplied by 8%. This result may be reduced by the market value of the option, subject to a maximum reduction to zero. 
Specific methods and treatments: Digital options
The option PRR for a digital option is the maximum loss of the option.
Specific methods and treatments: Written cliquet options
The option PRR for a written cliquet option is the market value of the derived position (see BIPRU 7.6.9R) multiplied by the appropriate position risk adjustment (see BIPRU 7.6.8R) multiplied by F+1 (see the following provisions of this paragraph). This result may be reduced by the amount the option is out of the money (subject to a maximum reduction to zero). The option PRR for a written cliquet option is therefore defined by the following formula:
[position risk adjustment * underlying * (F + 1)]  OTM
where:
 (1)
 (2)
FR= Number of forward resets
 (3)
Y= Years to maturity
 (4)
OTM= the amount by which the option is out of the money
Specific methods and treatments: Quantos
If the payout to the holder of a quanto option is fixed at the inception of the transaction a firm must add 8% to the position risk adjustment when applying the option standard method.
Interaction with other chapters
The application of an option PRR to a position does not prevent any of the other PRR charges from applying if they would otherwise do so. In particular if a firm applies an option PRR to an equity derivative an interest rate PRR will also generally apply.
Options on a commodity
BIPRU 7.4.38R to BIPRU 7.4.41R (Liquidity and other risks) apply to commodity options treated under BIPRU 7.6 as well as to those treated under BIPRU 7.4 (Commodity PRR).
Options on a CIU
For the purpose of identifying the appropriate treatment for the purpose of BIPRU 7.6.5R, the underlying position for the purpose of BIPRU 7.6.8R and the derived position under BIPRU 7.6.13R a firm may choose between treating an option on a CIU as being:
 (1)
 (2)
(if the conditions in BIPRU 7.7 (Position risk requirements for collective investment undertakings) for the use of the method in question are satisfied) positions in the underlying investments or assumed positions arising through the use of the standard CIU look through method or the modified CIU look through method.
 (1)
This paragraph gives an example of how the appropriate position risk adjustment should be calculated for the purpose of deciding whether or not an option on a CIU is sufficiently in the money for the firm to have a choice whether or not to apply an option PRR. This example assumes that there is no leveraging (see BIPRU 7.7.11R (CIU modified look through method)).
 (2)
Say that the CIU contains underlying equity position and the firm is using one of the CIU look through methods. The appropriate position risk adjustment for some is 8% and for the others is 12%. The firm should identify the highest appropriate position risk adjustment for the underlyings. In this case it is 12%. Therefore in this case the option would need to be in the money by more than 12% in order for the firm to have a choice between applying the option PRR or one of the other PRR charges.
 (3)
However if the firm is not using one of the CIU look through methods the option would need to be in the money by more than 32% in order for the firm to have a choice between applying the option PRR or the CIU PRR.
BIPRU 7.6.10R  BIPRU 7.6.12R are subject to BIPRU 7.7.3R (netting). BIPRU 7.7.4R (use of third party) applies for the purpose of BIPRU 7.6.