The standardised approach (SA) market risk capital charge calculation method is to come into effect from 2023 onwards. The calculation of market risk capital charge using the standardised method consists of determining a capital charge per risk class using the Sensitivities Based Approach (SBA) and aggregating them to determine the overall capital charge for market risk. To this are added the charge for the risk of default, as well as the additional charge for the residual risk to arrive at the minimum capital requirement as per the standardised approach.

Identify Risk Factors

• The first step is to identify, for all instruments held in the trading portfolio, the risk factors that apply and which risk buckets they belong to. 
• The next step is to calculate net sensitivities by risk factor for the instruments in the portfolio. The term “net” is important, meaning that we calculate the arithmetic sum of all Delta (respectively all Vega and Curvatures) calculated on a given risk factor in the trading portfolio. 
• As a result, sensitivities in opposite directions for a given risk factor compensate each other, which makes sense from the risk point of view: a position sensitive to a risk factor in one direction can be hedged by another position that varies in the opposite direction. In other words, within the same risk class and for the same indicator, the portfolio’s diversification effect is fully exploited to achieve capital charge “savings” when exposed to market risk.

Calculate Weighted Sensitivities 

Each net sensitivity is then assigned the risk weight provided in the documentation for the relevant risk factor and risk bucket to give the weighted sensitivity. 
For example, Risk Weighted Factors Sensitivities for GIRR Delta charge at currency level for each Tenor [k] will be calculated as

We can think of dividing PV01 by 0.0001 as converting a sensitivity into a ‘Notional-Equivalent’ to which a % Risk Weight is applied. Or we can think of the % RW divided by 0.001 as a bps scenario that is applied to a PV01.

Aggregate Sensitivities

a) By Bucket

Weighted sensitivities by risk bucket must then be aggregated. For Delta and Vega, the formula for calculating the capital charge for bucket b is as follows:

b) By Risk Class
The aggregation by risk class is done in a similar way using the results of the previous step and the correlation parameters between buckets within the same risk class:

Scenarios

This dual aggregation process must be carried out 3 times per risk class and indicator, with three different correlation scenarios: low, medium and high. For each indicator, the correlation scenario with the highest end result (Delta + Vega + Curvature, for all risk classes) will be retained. 

Using 3 scenarios makes it possible to take into account the fact that in times of market stress, correlations between risk factors may increase or decrease.

The total capital charge is equal to the sum of Delta, Vega and Curvature charges. The three capital charges are calculated for each of the three correlation scenarios, and the highest one is retained as the capital charge for market risk.

B. Default Risk Capital Charge Calculation

The default risk capital (DRC) requirement is intended to capture jump-to-default (J2TD) risk that may not be captured by credit spread shocks under the sensitivities-based method. DRC requirements provide some limited hedging recognition and banking book like treatment.

• The default risk capital charge for non-securitization and securitization is independent from the other capital charges in the SA for market risk, in particular from the credit spread risk (CSR) capital charge.
• The capital for the correlation trading portfolio (CTP) includes the default risk for securitization exposures and for non-securitization hedges. There must be no diversification benefit between the DRC for non-securitization, DRC for securitization (non-CTP) and DRC for the securitization CTP.
• At national discretion, claims on sovereigns, public sector entities and multilateral development banks may be subject to a zero default risk weight.
• For traded non-securitization credit and equity derivatives, JTD amounts by individual constituent issuer legal entity should be determined by applying a look-through approach.

Net jump-to-default risk positions (Net JTD) 

Exposures to the same obligator may be offset as follows:

• The gross JTD risk positions of long and short exposures to the same obligor may be offset where the short exposure has the same or lower seniority relative to the long exposure. For example, a short exposure in an equity may offset a long exposure in a bond, but a short exposure in a bond cannot offset a long exposure in the equity.
• For the purposes of determining whether a guaranteed bond is an exposure to the underlying obligor or an exposure to the guarantor, the credit risk mitigation requirements set out in paragraphs 189 and 190 of the Basel II framework apply.
• Exposures of different maturities that meet this offsetting criterion may be offset as follows:
  • Exposures with maturities longer than the capital horizon (one year) may be fully offset.
  • An exposure to an obligor comprising a mix of long and short exposures with a maturity less than the capital horizon (equal to one year) must be weighted by the ratio of the exposure’s maturity relative to the capital horizon. For example, with the one-year capital horizon, a three-month short exposure would be weighted so that its benefit against long exposures of longer-than-one-year maturity would be reduced to one quarter of the exposure size.

Net jump-to-default risk positions (Net JTD)

The following step-by-step DRC Calculation approach must be followed for each risk class subject to default risk – 

C. Residual Risk Add-On (RRAO) Capital Charge Calculation

The Residual risk add-on (RRAO) is to be calculated for all instruments bearing residual risk separately in addition to other components of the capital requirement under the FRTB Standardised Approach.

Conclusion

The institutions are faced with a multitude of adjustments and calibrations in their methodology of capital charge computation for market risk, however the Standarised Approach provides a credible alternative for trading desks to operate under a capital regime that is conservative, but not totally punitive. There is a complexity to factor for the banks considering to adopt the Standardised Approach capital charge calculation and looking to leverage their existing sensitivity-based VaR model, due to the difference between the existing sensitivity calculations and the prescribed FRTB formula. Unless it can be shown that the discrepancies between the 2 sets of formulae are minor, some analytical duplication might have to be undertaken, with a set of calculations for FRTB and another set for internal risk management.