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, 2018^{4}).

## 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.

*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:

- The assignment of the portfolio to risk classes;
- The identification of buckets;
- The estimation of net sensitivities
for each risk class;
- The calculation of weighted net sensitivities for
each risk factor;
- The computation of sensitivities for risk positions
within each bucket,
- the estimation of capital charge across buckets;
- The aggregation of the sensitivity risk charge based on correlation
scenarios (see Figure 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:

- A shock of increasing the level of correlations by 25%;
- No
shock, i.e. unchanged correlation;
- A shock of reducing the level of
correlations based on a formula proposed by the framework as proposed in the
latest amendments (BCBS, 2018
^{4}, 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).

*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,
2018^{4}, 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:

- A five-year maturity corporate bond with a modified
duration of 4.5, denominated in GBP;
- A two-year maturity government
bond with a modified duration of 2.8, denominated in GBP; and,
- 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:

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

- All assets are interest rate sensitive. As a result,
they fall under the GIRR risk class;
- 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;
- The sensitivities S
_{k},
S_{l} and S_{m} 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;
- By knowing the instruments’ maturity, the bank
identifies the vertexes, as of 5, 2 and 7, set by the framework;
- 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%];
- 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;
- 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;

- 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].
- The level of correlation across those buckets is
defined by the framework and set to a degree of 0.5;
- 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.

*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 **https://www.bis.org/publ/bcbs265.pdf*

*[3]>**Basel Committee on Banking Supervision
(BCBS). (2017, June). Simplified alternative to the standardised approach to
market risk capital requirements. Retrieved June 2017, from **https://www.bis.org/bcbs/publ/d408.pdf*