Read Part 1 here

Financial institutions must devote a
series of methods for implementing the standardized approach (SA) to
calculate the minimum capital requirements for Market Risk (FRTB) including
a) the sensitivities-based method (SbM), b) the default risk charge (DRC),
and c) the residual risks add-on (RRAO) methods. Part
one of this commentary series covered the SbM while this article will
focus on the principles for implementing the DRC following the BCBS
frameworks (BCBS, 2013^{1} , 2016^{2}, 2018^{3}).

## Standardized Default Risk Charge

Banks holding long
credit positions must analyze Mark-to-market (MTM) as well as jump to
default (JTD) risks, with the latter stating the default event that may
arise over time and the former denoting the daily fluctuations of the
credit spreads. Held-to-maturity exposures are more sensitive to JTD
risk given the extended time duration and thus the prospect for a
default event to occur. The resulting JTD risk losses strikes as a
sudden default credit event. The credit spread sensitivities expressed
using MTM risk analysis where deterministic shocks applied to credit
spreads, may be unable to capture the losses arising from a JTD
event.

This is why the final Basel III framework proposes
approaches for capturing sudden credit events and resulting losses
that are not encapsulated by applying shocks in credit spread when
using the MTM method but instead appear in the tail of the default
distribution. Moreover, measuring the impact of the sudden credit event
to exposure and resulting losses bank can hedge JTD risks. Recoveries
may also reduce the degree of credit losses and is therefore considered
in calculating JTD risk using the analysis parameters of the expected
recovery as it relates to the seniority of the specific credit
instrument.

Based on the new BCBS framework (2016, 2017) banks must
follow four-steps for calculating the standardized DRC of the trading
portfolios which containing both securitization and
non-securitization instruments (Figure 1):

- For each
instrument exposed to counterparty calculating the JTD loss
amounts;
- For the long and short exposures belonging to the
same obligor calculating the netting of the JTD risk amounts that
refer which resulting in the net long or net short JTD amount;
- Calculating the discounted hedge benefit ratio applied to net
short exposures;
- Applying the default RWs for calculating DRC
assuming no correlation to market risk.

*Figure
1: Steps for calculating the standardized DRC of the trading
portfolios*

Let us now explore the steps mentioned above and
understand how to calculate the DRC for non-securitizations. We are
initially going through the definitions, rules and formulae provided by
the framework and then applying them using an example case on trading
book portfolio.

## Default Risk Charge of Non-Securitizations

*Step 1: Calculating the gross JTD loss
amounts*The bank should calculate the gross JTD loss amounts
of non-securitization default risk as the higher of (a) the product of
LGD and long notional amount of the exposure plus the P&L amount
and (b) zero, or the lower of the (c) product of LGD and short
notional amount of the exposures plus the P&L amount, and (d)
zero.

JTD_{long}=max(LGD×notional+P&L;0)

*JTD*_{short}=min(LGD×notional+P&L;0)

*where*

## Scaling of JTD Maturity

Banks should also assume a time horizon of
one year for the exposures under JTD analysis. However, in case the
maturities are between three-month to one year, banks must scale up the
exposure to one year. Also, maturities that have a time horizon of less
than three months should be scaled up to maturity of three months.
Finally, the securities related to cash equity positions are supposed
to have a maturity of either three months or more than one year.

**Step 2: Net Jump-To-Default Risk Positions (Net
JTD)**Banks should also net the JTD exposures belong to the
same obligor based on rules driven by the maturity of the positions:

- By holding both short and long positions, the offsetting applies
only in the case that short exposures have equal or lower seniority to
the long exposures;
- Subject to the abovementioned restrictions,
in case that the maturities of the long or short exposures have less
than the one-year horizon, banks must weigh the capital horizon by the
ratio of the exposure’s maturity relative to time horizon.

The net JTD risk exposures are weighted according to their credit
quality^{4} and allocated to buckets of corporates, sovereigns,
and local governments/municipalities.

**Step 3: Hedge
benefit ratio to net short exposures**Any possible
hedging benefit between long and short positions belong to the same bucket
should also be calculated by the bank defined as hedge benefit ratio,
henceforth, weighted-to-short (WtS) ratio:

*where*

∑netJTD_{long} and ∑netJTD_{short} are the sums of
unweighted net long JTD and net short JTD amounts across the credit quality
categories.

The WtS is a discount factor of the function that
estimates the DRC.

**Step 4: Default Risk Capital Charge for
Non-Securitizations**Banks can calculate the default risk
charge *DRC*_{b} at the level of bucket *b* as the
difference between the sum (across the credit quality categories) of (a)
the risk-weighted long net JTD, and (b) the risk-weighted short net JTD
weighted by the WtS discounting factor; or zero.

Given that the new
framework disallows hedging between different buckets, the total capital
charge for default risk of non-securitizations is made up of the
aggregation capital charges of individual buckets.

## Example of
calculating Default Risk Capital Charge

Let us examine a case of
a banking institution which holds a trading book portfolio with the
following exposures:

- A long senior position,
*P*_{1}, of a pharmaceutical corporate bond which is maturing
in six years having a notional of EUR 30 million, hedged by a EUR 35
million short equity position, P_{2}, of pharmaceutical corporate
of the same issuer with a maturity of nine months. The rating of the
issuer is set to B while the level of *LGDs* is for
*P*_{1} set as *LGD*_{P(1)} =75% and for
*P*_{2} is set *LGD*_{P(2)}
=100%;
- A long CDS position,
*P*_{3}, used to
sell three-month protection of EUR 15 million against the default of a
B-rated Energy corporate, whose expected LGD is 100%;
- A short
position,
*P*_{4}, of EUR 10 million on a C-rated IT
company for three months;
- A long senior auto industrial
corporate bond position,
*P*_{5}, with notional of EUR 15
million, with credit quality A, with maturity of two years, and an
expected LGD of 75%;
- A long senior telecom corporate bond
position,
*P*_{6}, with notional of EUR 150 million
duration of two years, hedged by a EUR 150 million short position,
*P*_{7}, of bought protection against the default of the
same issuer for a duration of one year. The credit quality of the issuer
is A. The level of LGDs is for *P*_{6} set as
*LGD*_{P(6)} =75% and for *P*_{7} is set
*LGD*_{P(7)}=100%;

Following the steps
described above and illustrated numerically in Table I, the resulting
Default Risk Charge is *DRC*^{b}=EUR 0.302 million.

*Table I Calculating Steps to Default Risk Charge*

## Layout of a process for
implementing Basel III minimum capital requirements for calculating Default
Risk Capital Charge

There are few points to make in conclusion.
Firstly, the necessary input data need for calculating Default Risk
Capital Charge refer to the Maturity, Notional, Credit Quality of the
Issuer, seniority and corresponding LGD of the position. Secondly, the
definitions of maturity adjustments and Risk Weights defined by the
framework. The P&L resulted mainly based on the Face, MtM and Market
Value together with the volatility’s degrees. Gross and Net JTD as well as
*DRC*^{b} for both long and short positions are calculated
based on the formulae provided by the framework. Banks must also
apply aggregation within the buckets, and report associated capital
against risk and losses. The cycle process of implementing Basel III
minimum capital requirements for calculating DCC based on the
standardized approach is illustrated in Figure 2.

*Figure
2: Process steps of implementing Basel III minimum capital requirements for DRC
of the trading portfolios*

## Beyond the silos

As discussed
in part
one, the SbM measures the capital against seven risk classes whereas the
RRAO ensures the coverage of the remaining gap, correlation, and behavior
risks. Furthermore, separately from the market risks, banks must calculate DRC
for the trading book portfolios exposed to counterparty credit risk. This
siloed approach to calculation excludes any attention of possible dependences
across the different risk classes. While banks can simply aggregate, the
capital resulted from the SbM, DRC and RRAO approaches.

However,
financial institutions are increasingly integrating siloed ways of thinking to
deal with the undeniable shift regarding cultural and technological
challenges spurred by external regulatory and internal management pressures.
The higher the degree of integration, the more financial institutions are
benefit from a holistic and consistent view of their balance sheet,
earnings, capital, liquidity and leverage under normal and stress
conditions through time - to support more informed and confident decision
making. The FRTB regulation is no exception, especially given its ties to
the Basel III regulation.

Read Part 1 here

### References

^{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

^{2}Basel Committee on Banking Supervision (BCBS). (2016,
January). Minimum capital requirements for market risk. Retrieved January
2016, from https://www.bis.org/bcbs/publ/d352.pdf

^{3}Basel Committee on Banking Supervision (BCBS). (March 2018).
Revisions to the minimum capital requirements for market risk. Retrieved
March 2018, from https://www.bis.org/bcbs/publ/d436.pdf

^{4}The classification of the credit quality set by rating grades of
AAA, AA, A, BBB, BB, B, CCC, unrated, and defaulted to the default RWs of 0.5%,
2%, 3%, 6%, 15%, 30%, 50%, 15%, and 100%, respectively.