13.18	Banks must have a separate internal model to measure the default risk of trading book positions. The general criteria in [10.1] to [10.4] and the qualitative standards in [10.5] to [10.16] also apply to the default risk model.
13.19	Default risk is the risk of direct loss due to an obligor’s default as well as the potential for indirect losses that may arise from a default event.
13.20	Default risk must be measured using a value-at-risk (VaR) model.
	(1)	Banks must use a default simulation model with two types of systematic risk factors.
	(2)	Default correlations must be based on credit spreads or on listed equity prices. Correlations must be based on data covering a period of 10 years that includes a period of stress as defined in [13.5] and based on a one-year liquidity horizon.
	(3)	Banks must have clear policies and procedures that describe the correlation calibration process, documenting in particular in which cases credit spreads or equity prices are used.
	(4)	Banks have the discretion to apply a minimum liquidity horizon of 60 days to the determination of default risk capital (DRC) requirement for equity sub-portfolios.
	(5)	The VaR calculation must be conducted weekly and be based on a one-year time horizon at a one-tail, 99.9 percentile confidence level.
Banks are permitted to calibrate correlations to liquidity horizons of 60 days in the case that a separate calculation is performed for equity sub-portfolios and these desks deal predominately in equity exposures. In the case of a desk with both equity and bond exposures, for which a joint calculation for default risk of equities and bonds needs to be performed, the correlations need to be calibrated to a liquidity horizon of one year. In this case, a bank is permitted to consistently use a 60-day probability of default (PD) for equities and a one-year PD for bonds.
[13.20](2) states: “Default correlations must be based on credit spreads or on listed equity prices.” No additional data sources (eg rating time series) are permitted
[13.20](1) specifies that banks must use a default simulation model with two types of systematic risk factors. To meet this condition, the model always have two random variables that correspond to the systematic risk factors. Systematic risk in a DRC requirement model must be accounted for via multiple systematic factors of two different types. The rando variable that determines whether an obligor defaults must be an obligor-specific function of the systematic factors of both types and of an idiosyncratic factor. For example, in a Merton-type model, obligor i defaults when its asset return X falls below an obligor-specific threshold that determines the obligor’s probability of default. Systematic risk can be described via M systematic regional factors Yjreglon(j = 1, ... , M) and N systematic industry factors Yjindustry (j= 1, ... , N). For each obligor i, region factor loadings Bi,jregionand industry factor loadings Bi,jindustry that describe the sensitivity of the obligor’s asset return to each systematic factor need to be chosen. There must be at least one non-zero factor loading for the region type and at least one non-zero factor loading for the industry type. The asset return of obligor i can be represented as X? =ΣBi,jregion ∙ Yjregion +Σ Bi,jindustry ∙ Yjindustry+?? ∙??, where εi is the idiosyncratic risk factor and γi is the idiosyncratic factor loading.
Banks are permitted to use a 60-day liquidity horizon for all equity positions but are permitted to use a longer liquidity horizon where appropriate
13.21	All positions subject to market risk capital requirements that have default risk as defined in [13.19], with the exception of those positions subject to the standardised approach, are subject to the DRC requirement model.
	(1)	Sovereign exposures (including those denominated in the sovereign’s domestic currency), equity positions and defaulted debt positions must be included in the model.
	(2)	For equity positions, the default of an issuer must be modelled as resulting in the equity price dropping to zero.
13.22	The DRC requirement model capital requirement is the greater of:
	(1)	the average of the DRC requirement model measures over the previous 12 weeks; or
	(2)	the most recent DRC requirement model measure.
13.23	A bank must assume constant positions over the one-year horizon, or 60 days in the context of designated equity sub-portfolios.
The concept of constant positions has changed in the market risk framework because the capital horizon is now meant to always be synonymous with the new definition of liquidity horizon and no new positions are added when positions expire during the capital horizon. For securities with a maturity under one year, a constant position can be maintained within the liquidity horizon but, any maturity of a long or short position must be accounted for when the ability to maintain a constant position within the liquidity horizon cannot be contractually assured.
13.24	Default risk must be measured for each obligor.
	(1)	Probabilities of default (PDs) implied from market prices are not acceptable unless they are corrected to obtain an objective probability of default.51
	(2)	PDs are subject to a floor of 0.03%.
13.25	A bank’s model may reflect netting of long and short exposures to the same obligor. If such exposures span different instruments with exposure to the same obligor, the effect of the netting must account for different losses in the different instruments (eg differences in seniority).
13.26	The basis risk between long and short exposures of different obligors must be modelled explicitly. The potential for offsetting default risk among long and short exposures across different obligors must be included through the modelling of defaults. The pre-netting of positions before input into the model other than as described in [13.25] is not allowed.
13.27	The DRC requirement model must recognise the impact of correlations between defaults among obligors, including the effect on correlations of periods of stress as described below.
	(1)	These correlations must be based on objective data and not chosen in an opportunistic way where a higher correlation is used for portfolios with a mix of long and short positions and a low correlation used for portfolios with long only exposures.
	(2)	A bank must validate that its modelling approach for these correlations is appropriate for its portfolio, including the choice and weights of its systematic risk factors. A bank must document its modelling approach and the period of time used to calibrate the model.
	(3)	These correlations must be measured over a liquidity horizon of one year.
	(4)	These correlations must be calibrated over a period of at least 10 years.
	(5)	Banks must reflect all significant basis risks in recognising these correlations, including, for example, maturity mismatches, internal or external ratings, vintage etc.
13.28	The bank’s model must capture any material mismatch between a position and its hedge. With respect to default risk within the one-year capital horizon, the model must account for the risk in the timing of defaults to capture the relative risk from the maturity mismatch of long and short positions of less than one-year maturity.
13.29	The bank’s model must reflect the effect of issuer and market concentrations, as well as concentrations that can arise within and across product classes during stressed conditions.
13.30	As part of this DRC requirement model, the bank must calculate, for each and every position subjected to the model, an incremental loss amount relative to the current valuation that the bank would incur in the event that the obligor of the position defaults.
13.31	Loss estimates must reflect the economic cycle; for example, the model must incorporate the dependence of the recovery on the systemic risk factors.
13.32	The bank’s model must reflect the non-linear impact of options and other positions with material non-linear behaviour with respect to default. In the case of equity derivatives positions with multiple underlyings, simplified modelling approaches (for example modelling approaches that rely solely on individual jump-to-default sensitivities to estimate losses when multiple underlyings default) may be applied (subject to SAMA approval).
The simplified treatment applies only to equity derivatives.
13.33	Default risk must be assessed from the perspective of the incremental loss from default in excess of the mark-to-market losses already taken into account in the current valuation.
13.34	Owing to the high confidence standard and long capital horizon of the DRC requirement, robust direct validation of the DRC model through standard backtesting methods at the 99.9%/one-year soundness standard will not be possible.
	(1)	Accordingly, validation of a DRC model necessarily must rely more heavily on indirect methods including but not limited to stress tests, sensitivity analyses and scenario analyses, to assess its qualitative and quantitative reasonableness, particularly with regard to the model’s treatment of concentrations.
	(2)	Given the nature of the DRC soundness standard, such tests must not be limited to the range of events experienced historically.
	(3)	The validation of a DRC model represents an ongoing process in which supervisors and firms jointly determine the exact set of validation procedures to be employed.
13.35	Banks should strive to develop relevant internal modelling benchmarks to assess the overall accuracy of their DRC models.
13.36	Due to the unique relationship between credit spread and default risk, banks must seek SAMA approval for each trading desk with exposure to these risks, both for credit spread risk and default risk. Trading desks which do not receive SAMA approval will be deemed ineligible for internal modelling standards and be subject to the standardised capital framework.
13.37	Where a bank has approved PD estimates as part of the internal ratings-based (IRB) approach, this data must be used. Where such estimates do not exist, or SAMA determines that they are not sufficiently robust, PDs must be computed using a methodology consistent with the IRB methodology and satisfy the following conditions.
	(1)	Risk-neutral PDs should not be used as estimates of observed (historical) PDs.
	(2)	PDs must be measured based on historical default data including both formal default events and price declines equivalent to default losses. Where possible, this data should be based on publicly traded securities over a complete economic cycle. The minimum historical observation period for calibration purposes is five years.
	(3)	PDs must be estimated based on historical data of default frequency over a one-year period. The PD may also be calculated on a theoretical basis (eg geometric scaling) provided that the bank is able to demonstrate that such theoretical derivations are in line with historical default experience.
	(4)	PDs provided by external sources may also be used by banks, provided they can be shown to be relevant for the bank’s portfolio.
13.38	Where a bank has approved loss-given-default (LGD)52 estimates as part of the IRB approach, this data must be used. Where such estimates do not exist, or SAMA determines that they are not sufficiently robust, LGDs must be computed using a methodology consistent with the IRB methodology and satisfy the following conditions.
	(1)	LGDs must be determined from a market perspective, based on a position’s current market value less the position’s expected market value subsequent to default. The LGD should reflect the type and seniority of the position and cannot be less than zero.
	(2)	LGDs must be based on an amount of historical data that is sufficient to derive robust, accurate estimates.
	(3)	LGDs provided by external sources may also be used by institutions, provided they can be shown to be relevant for the bank’s portfolio.
13.39	Banks must establish a hierarchy ranking their preferred sources for PDs and LGDs, in order to avoid the cherry-picking of parameters.

⁵¹ Market-implied PDs are not acceptable.
⁵² LGD should be interpreted in this context as 1 – recovery rate.