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Foundations of FRTB for Market Risk — Part II

Ameya Abhyankar
8 min readDec 17, 2023



This article is the Part II of the article series discussing the Fundamental Review of the Trading Book (FRTB) guideline. In Part I of this article series, we discussed key foundational concepts and then discussed the Standardized Approach (SA) for calculation of capital for market risk. Click here to read Part I of this article series on FRTB

In this Part II of the series of articles on FRTB, we will discuss Internal Models Approach (IMA) for calculation of market risk capital charge under the FRTB guideline. The IMA approach is more dynamic vis-à-vis standardized approach as banks get an opportunity to apply their ideas for modelling risk to calculate the market risk capital for their trading desks. However, this opportunity for the bank to use its own internal models does not come easy. There are multiple supervisor-defined requirements that the bank not only needs to meet once at time of receiving approval, but has to continue to meet these conditions consistently going forward.

Let’s explore further details pertaining to the IMA approach in this article.

Internal Models Approach (IMA)

As mentioned in Part I article, every bank is expected to calculate the capital charge under the Standardized Approach (SA). Supervisory approval is not required for usage of SA. However, for usage of Internal Models Approach (IMA) by a bank, it requires explicit approval from supervisory authorities. There are a set of conditions that banks need to satisfy in order to be eligible for usage of IMA for capital purposes. Conditions are as given below:

The bank has a robust risk management system that is conceptually very sound and stable

The bank deploys models that can reasonably assess the risk on its book

The bank conducts stress testing regularly in compliance with Basel guidelines

The bank has sufficient number of skilled personnel in the areas of : Risk, Audit, compliance, trading, back office

The positions included in the internal models for regulatory capital determination are held in the approved trading desks and have successfully passed the tests as required by the Basel guidelines

Do all trading desks get to use the IMA?

Well, not all trading desks may get to use the IMA. There are certainly some desks that are simply not permitted to use the IMA, whereas, others may fail to meet the required criteria to qualify as ones using IMA. To get supervisory approval:

a. the bank needs to enlist the trading desks that are in-scope or out-of scope of the supervisory model approval process.

b. If a certain trading desk is in-scope of the IMA, then the bank has to assess the desk level model performance against P&L attribution and back-testing.

c. If all criteria are met, then the bank needs to analyze modellable and non-modellable risk factors (more about this coming up below).

As mentioned earlier, few desks are simply not allowed to use IMA. For example, securitization exposures have to be considered under SA only and are out of scope for IMA.

Modellable and Non-modellable risk factors:

Modellable risk factors:

These are a set of risk factors that are subject to capital charge under the IMA. Capital charge for Expected Shortfall (ES) plus the capital charge for Default Risk Charge (DRC) make up for the capital charge attributable to modellable risk factors

Non-modellable risk factors:

These are subject to stress scenarios under IMA. Stressed capital add-on is the regulatory capital charge for non-modellable risk factors

The guideline lays down conditions for risk factors to be bifurcated into one of the two buckets. Amongst other things, the main point that differentiates between these two classes has to do with the frequency (read liquidity) of the risk factor. As one may expect, capital charge for non-modellable risk factors is higher than capital charge for modellable risk factors. Think of non-modellable risk factors as ones that do not get to enjoy the benefits of market liquidity, and thus end up attracting higher capital charge vis-à-vis modellable risk factors.

Overall Capital Charge under IMA =

Risk Charge for Expected Shortfall


Risk Charge for Default Risk Charge


Risk Charge for Stressed Capital Add-on


SA capital charge for risks from non-approved trading desks

Risk Charge for Expected Shortfall

Expected Shortfall (ES) is a conditional probability measure of risk. For readers familiar with the Value at Risk (VaR) models, ES is just a step ahead i.e. it attempts to answer the question that if VaR is breached on a certain day, how bad can things get. ES is a representative of average of tail losses. The advantage is a ES also satisfies the criteria of a spectral risk measure. Spectral risk measures are coherent and have their own advantages when quantifying the risk of a portfolio.

Liquidity Horizon (LH) is a key input while calculating the Expected Shortfall (ES), the FRTB guideline does not follow a static time horizon for liquidity, rather it allows for a range of time horizons to better capture the risk in the bank’s portfolio (i.e. enables to factor-in market liquidity conditions). By definition, LH is defined as the time required to exit OR hedge a position without too much impact on market prices, under stressed market conditions. BCBS guideline give the formula to be used for ES calculation after inclusion of the liquidity horizon as one of the input.

The FRTB regulation specifies guidance for banks and supervisory authorities to follow while computing the ES

Guidance for Banks

  • Banks are expected to hold on a daily basis a capital requirement which is equal to: maximum (previous day’s capital charge , an average of daily capital charge over previous 60 days)
  • The ES model should be robust and should be able to capture all the risks on their books
  • A scaled ES measure should be calculated based on the Liquidity Horizons as defined by the guideline
  • Correlations used between Risk Factor classes namely GIRR, CSR, FX, Equity and Commodity should be used in a consistent manner & be clearly documented

Guidance for supervisory authorities

  • Have the authority to tell banks as to which model they should use: Historical simulation, Monte carlo, other analytical methods

As mentioned above, ES capital charge is one of the components of market risk charge that is attributable to modellable risk factors. A standard formulation of aggregate capital charge for modellable risk factors (IMCC) is given in the guideline as below:

Where IMCC (C ): unconstrained ES charge

IMCC (C(i)): partial, constrained ES charges

i: Index of the 5 risk classes

ρ: Relative weight assigned to the bank’s internal model

Default Risk Capital Charge (DRC)

The FRTB guideline has introduced the DRC for IMA (this replaces the IRC which was used earlier). Expected Shortfall fails to capture the risk of default of instruments, therefore, we need to calculate the DRC in addition to it.

As per the guideline, the DRC requirement will be the greater of:

  1. Average DRC measure over the last 12 months
  2. Most recent DRC measure

Banks must have a separate Internal Model to measure Default Risk of Trading Book positions

Banks must measure their default risk using a VaR model:

  1. Time horizon — 1 year
  2. Confidence Interval — 99.9%
  3. On a weekly basis

Readers familiar with credit risk modelling concepts will be aware of following ideas:

a. Probability of Default (PD)

b. Loss Given Default (LGD)

c. Default correlations

d. Hedging benefits

The above four components are used in the calculation of the DRC component of market risk charge. Further, the FRTB guideline specifies the exact treatment for handling of the above four components for measuring the DRC.

Capital charge for non-modellable risk factors

Each factor, the Liquidity Horizon of the stress scenario must be greater of the following two:

  1. Liquidity horizon assigned to the risk factor
  2. Largest time interval between 2 consecutive price observations over the prior year

Each factor should be capitalized using a stress scenario that is calibrated to be atleast as prudent as the ES calibration for modellable risks (i.e. loss calibrated to 97.5% confidence interval over a period of extreme stress)

Where, NMRF: Aggregate capital measure for non-modellable risk factors

L: Non-modellable idiosyncratic credit risk factors (to be aggregated with 0 risk correlation)

INFRM i: Capital charge for stress scenario for idiosyncratic credit spread non-modellable risk i from the L risk factors aggregated with 0 correlation

k: Non-modellable risk factors in model eligible trading desks

NMRF j: Capital charge from stress scenario for non-modellable risk j

Specification of Market Risk Factors

Banks are expected to meet a certain requirements when specifying the risk factors for capital calculations. This is important because an incorrect choice of risk factors can misstate risk

FRTB guidelines specify the exact set of conditions to be satisfied while choosing the set of market risk factors for the 5 risk classes namely GIRR, CSR, Equity, FX, commodity.

Model Validation Standards

The IMA requires banks to periodically get their models validated by qualified and external/independent internal teams

The validation needs to be done when:

  1. There are significant structural changes in the market
  2. Significant changes in the composition of the portfolio

Validation will include review of the following:

  1. Back testing results
  2. P&L attribution
  3. Any other tests that are used to demonstrate that assumptions made (if any) are appropriate and do not under-estimate risk

Model validation must use hypothetical changes in the portfolio value in cases where the EoD positions remain unchanged

P&L attribution

  • Every Trading Desk must satisfy the P&L attribution requirement
  • Under P&L attribution, there are two ratios of unexplained P&L. The breaches in these two ratios have to be monitored throughout the year

The unexplained P&L is defined as the difference between the following:

If a trading desk observes more than 4 breaches within the last 12 months, then it should calculate capital charge using the Standardized Approach (SA)


Model back testing is vital in order to understand if the model is capable enough to quantify the risk sitting on the bank’s portfolio.

FRTB places a lot of importance of daily back testing of the risk model, so that banks are confident of the risk models that they use for measurement of capital charge

Model back-testing is to be performed daily

  • It is done for both 99% and 97.5% 1-day VaR
  • Portfolio are tested both at the trading desk level and the bank-wide level

Banks are expected to do back testing basis both : hypothetical and actual trading outcomes

If in the most recent 12 months period a desk has experienced either of the following:

  • More than30 exceptions at 97.5%
  • More than 12 exceptions at 99%

Then the trading desk is required to calculate capital charge based on Standardized Approach (SA)


This article discusses the foundational aspects of Internal Models Approach (IMA) for FRTB. Although the IMA approach appears attractive enabling banks flexibility for using their own internal models for risk measurement, many global banks are contemplating whether using the Standardized Approach (SA) would be an easier way out. The banks will need weigh the benefits of using the IMA vis-à-vis the simplicity that SA provides in the capital charge calculations. However, from the point of view of a banker, consultant, business analyst or any other student of banking & finance, its important that they are familiar with both the Standardized Approach (SA) as well as Internal Models Approach (IMA) under FRTB. Knowledge of both of the aforementioned approaches has the potential to work on projects in these domains and also apply for new job roles in risk management that demand knowledge of this new regulatory guideline.