Sensitivities-based method: definition of sensitivities
7.15	Sensitivities for each risk class must be expressed in the reporting currency of the bank.
7.16	For each risk factor defined in [7.8] to [7.14], sensitivities are calculated as the change in the market value of the instrument as a result of applying a specified shift to each risk factor, assuming all the other relevant risk factors are held at the current level as defined in [7.17] to [7.38].
As per [7.17], a bank may make use of alternative formulations of sensitivities based on pricing models that the bank’s independent risk control unit uses to report market risks or actual profits and losses to senior management. In doing so, the bank is to demonstrate to SAMA that the alternative formulations of sensitivities yield results very close to the prescribed formulations.
Requirements on instrument price or pricing models for sensitivity calculation
7.17	In calculating the risk capital requirement under the sensitivities-based method in [7], the bank must determine each delta and vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management.
[7.17] states that banks must determine each delta sensitivity, vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management. Banks should use zero rate or market rate sensitivities consistent with the pricing models referenced in that paragraph.
7.18	A key assumption of the standardised approach for market risk is that a bank’s pricing models used in actual profit and loss reporting provide an appropriate basis for the determination of regulatory capital requirements for all market risks. To ensure such adequacy, banks must at a minimum establish a framework for Prudent Valuation Guidance set out in Basel Framework .
Sensitivity definitions for delta risk
7.19	Delta GIRR: the sensitivity is defined as the PV01. PV01 is measured by changing the interest rate r at tenor t (rt) of the risk-free yield curve in a given currency by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument (Vi) by 0.0001 (ie 0.01%) as follows, where:
	(1)	rt is the risk-free yield curve at tenor t;
	(2)	cst is the credit spread curve at tenor t; and
	(3)	Vi is the market value of the instrument i as a function of the risk-free interest rate curve and credit spread curve:
7.20	Delta CSR non-securitisation, securitisation (non-CTP) and securitisation (CTP): the sensitivity is defined as CS01. The CS01 (sensitivity) of an instrument i is measured by changing a credit spread cs at tenor t (cst) by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument (Vi) by 0.0001 (ie 0.01%) as follows:
In cases where the bank does not have counterparty-specific money market curves, the bank can proxy PV01 to CS01
7.21	Delta equity spot: the sensitivity is measured by changing the equity spot price by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument (Vi) by 0.01 (ie 1%) as follows, where:
	(1)	k is a given equity;
	(2)	EQk is the market value of equity k; and
	(3)	Vi is the market value of instrument i as a function of the price of equity k.
7.22	Delta equity repo rates: the sensitivity is measured by applying a parallel shift to the equity repo rate term structure by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument Vi by 0.0001 (ie 0.01%) as follows, where:
	(1)	k is a given equity;
	(2)	RTSk is the repo term structure of equity k; and
	(3)	Vi is the market value of instrument i as a function of the repo term structure of equity k.
7.23	Delta commodity: the sensitivity is measured by changing the commodity spot price by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument Vi by 0.01 (ie 1%) as follows, where:
	(1)	k is a given commodity;
	(2)	CTYk is the market value of commodity k; and
	(3)	Vi is the market value of instrument i as a function of the spot price of commodity k:
7.24	Delta FX: the sensitivity is measured by changing the exchange rate by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument Vi by 0.01 (ie 1%), where:
	(1)	k is a given currency;
	(2)	FXk is the exchange rate between a given currency and a bank’s reporting currency or base currency, where the FX spot rate is the current market price of one unit of another currency expressed in the units of the bank’s reporting currency or base currency; and
	(3)	Vi is the market value of instrument i as a function of the exchange rate k:
Sensitivity definitions for vega risk
7.25	The option-level vega risk sensitivity to a given risk factor18 is measured by multiplying vega by the implied volatility of the option as follows, where:
	(1)	vega, ∂vi/∂σi, is defined as the change in the market value of the option Vi as a result of a small amount of change to the implied volatility σi, and
	(2)	the instrument’s vega and implied volatility used in the calculation of vega sensitivities must be sourced from pricing models used by the independent risk control unit of the bank.
7.26	The following sets out how to derive vega risk sensitivities in specific cases:
	(1)	Options that do not have a maturity, are assigned to the longest prescribed maturity tenor, and these options are also assigned to the RRAO.
	(2)	Options that do not have a strike or barrier and options that have multiple strikes or barriers, are mapped to strikes and maturity used internally to price the option, and these options are also assigned to the RRAO.
	(3)	CTP securitisation tranches that do not have an implied volatility, are not subject to vega risk capital requirement. Such instruments may not, however, be exempt from delta and curvature risk capital requirements.
Under the sensitivities-based method and In the case where options do not have a specified maturity (eg cancellable swaps), the bank must assign those options to the longest prescribed maturity tenor for vega risk sensitivities and also assign such options to the RRAO.
In the case of the bank viewing the optionality of the cancellable swap as a swaption, the bank must assign the swaption to the longest prescribed maturity tenor for vega risk sensitivities (as it does not have a specified maturity) and derive the residual maturity of the underlying of the option accordingly.

¹³ The assignment of risk factors to the specified tenors should be performed by linear interpolation or a method that is most consistent with the pricing functions used by the independent risk control function of a bank to report market risks or P&L to senior management.
¹⁴ Cross-currency basis are basis added to a yield curve in order to evaluate a swap for which the two legs are paid in two different currencies. They are in particular used by market participants to price cross-currency interest rate swaps paying a fixed or a floating leg in one currency, receiving a fixed or a floating leg in a second currency, and including an exchange of the notional in the two currencies at the start date and at the end date of the swap.
¹⁵ For example, an option with a forward starting cap, lasting 12 months, consists of four consecutive caplets on USD three month Libor. There are four (independent) options, with option expiry dates in 12, 15, 18 and 21 months. These options are all on underlying USD three-month Libor; the underlying always matures three months after the option expiry date (its residual maturity being three months). Therefore, the implied volatilities for a regular forward starting cap, which would start in one year and last for 12 months should be defined along the following two dimensions: (i) the maturity of the option’s individual components (caplets) – 12, 15, 18 and 21 months; and (ii) the residual maturity of the underlying of the option – three months.
¹⁶ For example, a contract that can be delivered in five ports can be considered having the same delivery location as another contract if and only if it can be delivered in the same five ports. However, it cannot be considered having the same delivery location as another contract that can be delivered in only four (or less) of those five ports.
¹⁷ For example, for an FX forward referencing USD/JPY, the relevant risk factors for a CAD- reporting bank to consider are the exchange rates USD/CAD and JPY/CAD. If that CAD- reporting bank calculates FX risk relative to a USD base currency, it would consider separate deltas for the exchange rate JPY/USD risk and CAD/USD FX translation risk and then translate the resulting capital requirement to CAD at the USD/CAD spot exchange rate.
¹⁸ As specified in the vega risk factor definitions in [7.8] to [7.14], the implied volatility of the option must be mapped to one or more maturity tenors.
¹⁹ Since vega (, ∂v/∂σi) of an instrument is multiplied by its implied volatility ( ), the vega risk sensitivity for that instrument will be the same under the log-normal assumption and the normal assumption. As a consequence, banks may use a log-normal or normal assumption for GIRR and CSR (in recognition of the trade-offs between constrained specification and computational burden for a standardised approach). For the other risk classes, banks must only use a log-normal assumption (in recognition that this is aligned with common practices across jurisdictions).
²⁰ In other words, a bank can initially not apply a look-through approach, and later decide to apply it. However once applied (for a certain type of instrument referencing a particular index), the bank will require SAMA approval to revert to a “no look-through” approach.
²¹ As specified in the vega risk factor definitions in [7.8] to [7.14], the implied volatility of an option must be mapped to one or more maturity tenors.