Prudential Regulation Authority Rulebook

1.

Institutions shall calculate the supervisory delta as follows:

1. (a) for call and put options that entitle the option buyer to purchase or sell an underlying instrument at a positive price on a single or multiple dates in the future, except where those options are mapped to the interest rate risk category, institutions shall use the following formula:

1. where:
2. δ = the supervisory delta;
3. sign = – 1 where the transaction is a sold call option or a bought put option;
4. sign = + 1 where the transaction is a bought call option or sold put option;
5. type = – 1 where the transaction is a put option;
6. type = + 1 where the transaction is a call option;
7. N(x) = the cumulative distribution function for a standard normal random variable meaning the probability that a normal random variable with mean zero and variance of one is less than or equal to x;
8. P = the spot or forward price of the underlying instrument of the option; for options the cash flows of which depend on an average value of the price of the underlying instrument, P shall be equal to the average value at the calculation date;
9. K = the strike price of the option;
10. T = the period between the expiry date of the option (Texp) and the calculation date; for options which can be exercised at one future date only, Texp is equal to that date; for options which can be exercised at multiple future dates, Texp is equal to the latest of those dates; T shall be expressed in years using business days;
11. σ = the supervisory volatility of the option determined in accordance with Table 1 on the basis of the risk category of the transaction and the nature of the underlying instrument of the option; and
12. λ = the presumed lowest possible extent to which prices of the underlying instrument of the option can become negative. The same parameter must be used consistently for all options in the same underlying instrument. For options on interest rates, the same parameter must be used consistently for all options in the same currency.
1. Table 1

2. Risk category	Underlying instrument	Supervisory volatility
   Interest rate	All	50%
   Foreign exchange	All	15%
   Credit	Single-name instrument	100%
   	Multiple names instrument	80%
   Equity	Single-name instrument	120%
   	Multiple names instrument	75%
   Commodity	Electricity	150%
   	Other commodities (excluding electricity)	70%
   Others	All	150%

3. Institutions using the forward price of the underlying instrument of an option shall ensure that:
1. (i) the forward price is consistent with the characteristics of the option;
2. (ii) the forward price is calculated using a relevant interest rate prevailing at the calculation date;
3. (iii) the forward price integrates the expected cash flows of the underlying instrument before the expiry of the option;
4. (b) for tranches of a synthetic securitisation and a nth-to-default credit derivative, institutions shall use the following formula:
1. 
2. where:
3. 
4. A = the attachment point of the tranche; for a nth-to-default credit derivative transaction based on reference entities k, A = (n – 1)/k; and
5. D = the detachment point of the tranche; for a nth-to-default credit derivative transaction based on reference entities k, D = n/k;
5. (c) for transactions not referred to in point (a) or (b), institutions shall use the following supervisory delta:

2.

For the purposes of this Section, a long position in the primary risk driver or in the most material risk driver in the given risk category for transactions referred to in Article 277(3) means that the market value of the transaction increases when the value of that risk driver increases and a short position in the primary risk driver or in the most material risk driver in the given risk category for transactions referred to in Article 277(3) means that the market value of the transaction decreases when the value of that risk driver increases.

3.

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