Finance26/07/2018 9:15:00 AM

Basel III Minimum Capital Requirements for Market Risk (FRTB)

Trading positions often face significant financial loss due to their exposure to volatilities present in underlying market risk factors. As it stands today, the trading book fails to capture the severity of such losses adequately, which has spurred the BCBS to propose a framework for the estimation of the minimum capital requirements for market risk, also known as the Fundamental Review of the Trading Book, more commonly known as FRTB (BCBS, 2013[1], 2016[2], 2017[3]). Moreover, the Basel Committee is currently monitoring and revising the implementation of the market risk standard, and proposing updated methods (BCBS, 2018[4]).

Market liquidity risk plays a key role in both the standardized approach (SA) and the internal model approach (IMA). In the IMA the framework introduces the expected shortfall (ES), substituting the value at risk (VaR) as a measure for the measurement of market risk. The new framework also introduces a profit and loss attribution (PLA) test that the trading desk must pass if they want to implement IMA.

Banks do not only have to estimate capital against the exposure to modellable risk factors. The framework now recognizes an additional capital requirement dedicated to non-modellable risk factors (NMRFs).

To ensure banks do not create regulatory arbitrage, the new framework aims to close the gaps between the treatment of trading and banking book exposures. To this end updated revisions to the boundary between the two books have been proposed by the committee (BCBS, 20184).

The Standardized Approach to Market Risk

Banks must devote a series of methods for implementing the standardized approach (SA) (Figure 1): a) the sensitivities-based method (SbM), b) the default risk charge (DRC), and c) the residual risks add-on (RRAO) methods. The committee also proposes a simplified alternative standardized approach to market risk.

FRTB Commentary Fig.1

Figure 1: Methods for implementing the standardized approach

Sensitivities-based Method

The SbM framework suggests that banks use sensitivity analysis for the estimation of capital charges against delta, vega, and curvature risks.

Banks should follow several steps for estimating the capital charges based on SbM. These steps include:

  1. The assignment of the portfolio to risk classes;
  2. The identification of buckets;
  3. The estimation of net sensitivities for each risk class;
  4. The calculation of weighted net sensitivities for each risk factor;
  5. The computation of sensitivities for risk positions within each bucket,
  6. the estimation of capital charge across buckets;
  7. The aggregation of the sensitivity risk charge based on correlation scenarios (see Figure 2).

FRTB Commentary Fig.2

Figure 2: Main steps for estimating capital charge based on the sensitivities-based method

Delta and vega risk charges are computed individually for seven risk classes, the capital charges within each bucket are aggregated and finally the capital requirements across those buckets is calculated. The weighted delta and vega sensitivities drive the capital on risk factors (RFs) and the correlation factors with and across buckets.

Banks also need to capture risks assigned to non-linear instruments which means they must estimate curvature risk dealing with the second-order sensitivity measurements. Thus, any changes in the price of an option not identified by delta and vega risk is addressed by curvature risk. The final Basel III framework approximates the curvature as an incremental capital charge above delta capital charge.

After estimating the curvature risk charge, banks have to apply the sensitivity risk charge aggregation based on three scenarios on the correlations between risk factors within a bucket and cross-bucket correlations within a risk class. In fact, the bank has to stress the correlation factors based on three scenarios:

  1. A shock of increasing the level of correlations by 25%;
  2. No shock, i.e. unchanged correlation;
  3. A shock of reducing the level of correlations based on a formula proposed by the framework as proposed in the latest amendments (BCBS, 20184, Annex A: 15 paras 54c).

Banks have to implement the above three scenarios individually for each risk class to calculate the risk charges accordingly. A portfolio exposed to risk classes must aggregate the associated risk charges and the three scenario-based risk charges resulting in three values of the aggregated portfolio. The highest of the three aggregated values is the recognized capital charge at portfolio level (Figure 3).

 FRTB Commentary Fig.3

Figure 3: The three steps for estimating of the sensitivity risk charge at the portfolio level

Grounded by evidential eligibility criteria, a simplified reduced SbA may be an alternative option for banks. The absence of vega estimation and curvature risks, and the reduction of RFs and correlation scenarios under consideration are both benefits of the less demanding framework, however, the upsurge of risk weights under this method means the capital charge rises significantly.

In the latest proposed amendments, further to alternative reduced SbA, the committee recommends a second alternative option whereby a recalibrated version of the Basel II standardized approach can be used (BCBS, 2018). It includes four multiplication scaling factors applied respectively to the capital requirements, estimated by the SA, in the four risk classes: FX risk, commodity risk, general and specific interest rate risk, general and specific equity risk. The over capital requirement results in summing up the recalibrated capital estimations (BCBS, 20184, Annex F: 39 paras 3).

Example of the Estimation of Delta Capital Charge

Let us examine a case of a banking institution based in the Euro-zone area that holds a portfolio consisting of three assets:

  1. A five-year maturity corporate bond with a modified duration of 4.5, denominated in GBP;
  2. A two-year maturity government bond with a modified duration of 2.8, denominated in GBP; and,
  3. A seven-year maturity corporate bond with a modified duration of 6.7, denominated in EUR.

By employing SbM the bank estimates delta general interest rate risk (GIRR) capital charges following the steps presented below and as illustrated in Table I:

 FRTB Commentary Fig.4

Table I. Steps of estimating the delta (GIRP) capital charge

  1. All assets are interest rate sensitive. As a result, they fall under the GIRR risk class;
  2. In the view of the bucket definition of GIRR delta the two currencies, that is, GBP and EUR, define two buckets, b1 and b2, accordingly;
  3. The sensitivities Sk, Sl and Sm denominated to GBP and EUR are approximated to the modified duration of the instruments, defined at the degrees of 4.5, 2.8 and 6.7 respectively;
  4. By knowing the instruments’ maturity, the bank identifies the vertexes, as of 5, 2 and 7, set by the framework;
  5. Corresponding to the above vertexes risk weights (RWs), distinct by the framework, are within a range of [0.90% - 1.20%], [1.10%  - 1.50%] and [0.90%  - 1.20%];
  6. The weighted sensitivities are estimated (BCBS, 2016[5] 25 paras 67), within a range of [0.041 - 0.054], [0.031 - 0.042] and [0.060 - 0.080], respectively;
  7. At the level of each bucket:

    - For assets one and two, the correlations between the two weighted sensitivities set to the range of [0.941 - 0.941] as derived from the rules defined by the framework (note that as b2 contains only one asset, a correlation factor is out of consideration);

    - For all assets, the risk positions are calculated resulting of a range within [0.070 - 0.095] for b1, and [0.004 - 0.006] for b2;

  8. The sensitivities for all risk factors for b1 are estimated within a range of [0.0713 - 0.096] for assets one and two, whereas asset three belongs to bucket b2 calculated within a range of [0.0603 - 0.0804].
  9. The level of correlation across those buckets is defined by the framework and set to a degree of 0.5;
  10. The delta capital charge estimated to the range of values between 0.096 and 0.129.

Layout of a process for implementing Basel III minimum capital requirements for market risk

In conclusion, initially banks must apply the necessary analytics for estimating the market risk sensitivities, classify the risk exposures and the assets under study to identify the associated risk weights, calculate the risk capital charge based on the formulas provided by the framework, apply aggregation rules within and across buckets, report associated capital against risk and losses. The cycle process of implementing Basel III minimum capital requirements for market risk based on the standardized approach is illustrated in Figure 4.

FRTB Commentary Fig.5

Figure 4: Process steps of implementing Basel III minimum capital requirements for Market Risk

[1]Basel Committee on Banking Supervision (BCBS). (2013, October). Fundamental review of the trading book: A revised market risk framework. Retrieved October 2013, from

[2]Basel Committee on Banking Supervision (BCBS). (2016, January). Minimum capital requirements for market risk. Retrieved January 2016, from

[3]>Basel Committee on Banking Supervision (BCBS). (2017, June). Simplified alternative to the standardised approach to market risk capital requirements. Retrieved June 2017, from

[4]Basel Committee on Banking Supervision (BCBS). (March 2018). Revisions to the minimum capital requirements for market risk. Retrieved March 2018, from

[5] Basel Committee on Banking Supervision (BCBS). (2016, January). Minimum capital requirements for market risk. Retrieved January 2016, from

by Ioannis Akkizidis, Product Manager, Risk and Finance, Wolters Kluwer
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