Calculation of Market Risk Capital Charge under FRTB

1. Ramesh Jonnadula

2. FRTB – Overview of Key Rules/Changes
 More Granular Model Approval Process
 Internal Model Approvals/revocation will be done at Trading Desk level as
compared to current Bank level IMA approvals
 IMA eligible desks will be subjected to new P&L attribution tests in
addition to Back-testing
 Overhaul of IMA
 Replace VaR and SVaR (Stressed VaR) with one single measure: Expected
Shortfall (ES)
 Expected Shortfall based on a 1-year stress period relevant for today's
portfolio, i.e., ever expanding historical window
 Capture of liquidity risk
 Liquidity is defined at risk factor level, not position level
 Liquidity horizons are prescribed by FRTB: 10, 20, 40, 60, 120
 Constraints on the effects of hedging and portfolio diversification:
Diversification across asset classes FX, IR, EQ, CR, CM is restricted.
 Replace IRC with DRC – no double counting of Credit Migration Risk
 Abandon CRM in favor of Standardized Charge

3. FRTB Market Risk Capital Charge
Components

4. Basel 2.5 vs FRTB
Basel 2.5 FRTB
IMA Approach
VaR
Expected Shortfall (ES)
Stressed VaR
Incremental Risk Charge
(IRC)
Default Risk Charge
(DRC)
RNiV by some regulators
Stress Capital Addon
(NMRF)
OR AND
Standardized
Approach
Standardized Charge
CRM
Sensitivity based Charge
Default Risk Charge
(DRC)
None Residual Risk Addon

5. Capital Charge
Aggregate Capital Charge
The aggregate capital charge for market risk (ACC) is equal to the aggregate
capital requirement for IM Approved trading desks plus the standardised capital
charge for risks from unapproved trading desks.
ACC = CA + DRCA + CU + DRCU
where
CA = Capital Charge for Internal Model Approved Trading Desks
DRCA = Default Risk Charge for Internal Model Approved Trading Desks
CU = Aggregate Standardised Capital Charge for Unapproved Trading Desks
DRCU = Standardised Default Risk Charge (for unapproved desks)

6. Capital Charge for Standardized Approach
Aggregate Capital Charge for Standardized Approach
The Aggregate Standardized Capital Charge for unapproved Trading desks
Standardized Charge (CU) = Sensitivities based Charge
+ Residual Risk Add-on

7. Capital Charge for IMA
Capital Charge for Internal Model Approach
The aggregated charge associated with approved desks (C 𝐴) is equal to the maximum
of the most recent observation and a weighted average of the previous 60 days scaled
by a multiplier (mc):
C 𝐴 = max( (IMCCt-1 + SESt-1) , (mc . IMCC60DayAvg + SES60DayAvg) )
where
IMCC is Capital Charge for Modellable riskfactors of IM approved desks
SES is Stressed Capital Addon for Non-Modellable risk factors of IM
Approved Trading Desks
The multiplication factor mc >= 1.5 and will be set by individual supervisory
authorities on the basis of their assessment of the quality of the bank’s risk
management system

8. Capital Charge for IMA
Capital Charge for Modellable Riskfactors under IMA
The capital charge for modellable risk factors (IMCC) is based on the weighted
average of the constrained and unconstrained expected shortfall charges
IMCC = 𝜌 . ESunconstrained + (1- 𝜌) . ESconstrained
where
ESunconstrained = ESTotal(AllRfs) (ES for all Risk factors honoring diversification)
ESconstrained = ESIR + ESCR + ESEQ + ESFX + ESCM (Sum of individual ES for all
risk classes)
𝜌 is the relative weight assigned to the firm's internal model, which is
currently set as 0.5.

9. Standardized Charge – Sensitivities based
Charge
Sensitivities based Charge (SBC)
In order to address the risk that correlations increase or decrease in periods of financial
stress, three correlation scenarios: high, medium and low correlations are considered and
Sensitivities based Risk charge for a given portfolio will be largest of these three charges
Sensitivities based Charge = max (Sensitivities based Charge(high corr),
Sensitivities based Charge(medium corr),
Sensitivities based Charge (low corr))
Sensitivities based Charge for a given Correlation Scenario = sum of Delta, Vega and Curvature
Risk Charges across all Risk Classes (IR, CR, EQ, FX & CM)
which is
Delta Risk Charge(IR) + Vega Risk Charge(IR) + Curvature Risk Charge(IR)
+ Delta Risk Charge(CR) + Vega Risk Charge(CR) + Curvature Risk Charge(CR)
+ Delta Risk Charge(EQ) + Vega Risk Charge(EQ) + Curvature Risk Charge(EQ)
+ Delta Risk Charge(FX) + Vega Risk Charge(FX) + Curvature Risk Charge(FX)
+ Delta Risk Charge(CM) + Vega Risk Charge(CM) + Curvature Risk Charge(CM)

10. SBC – Delta & Vega Risk Charges
Delta &Vega Risk Charges
 Calculate net sensitivity 𝑠 𝑘 across instruments to each risk factor k
(decompose ndex instruments and multi-underlying options).
 Assign Risk weights (R𝑊 𝑘) to each Riskfactor and compute weighted sensitivity
𝑊S 𝑘 as
 Group the Riskfactors in a given Risk Class into buckets. The risk position for
Delta bucket b (respectively Vega), 𝐾 𝑏, computed using correlation between
riskfactors (𝜌 𝑘l) using the following formula:
If the value inside the square root is –ve, 𝐾 𝑏 = 0
 The Delta (respectively Vega) risk charge for a given Risk Class (IR, CR, ..) is
computed using bucket correlations (γbc):
where Sb=Σ 𝑘 𝑊S 𝑘 for all risk factors in bucket b and Sc=Σ 𝑘 𝑊S 𝑘 in bucket c.. If the
value inside square root is –ve, use the following
Sb = max [min(Σ 𝑘 𝑊S 𝑘, 𝐾 𝑏), − 𝐾 𝑏] Sc= max [min(Σ 𝑘 𝑊S 𝑘, 𝐾c), − 𝐾c]

11. SBC – Curvature Risk Charge
Curvature Risk Charge
Curvature risk is based on two stress scenarios involving an upward shock and a
downward shock to a given risk factor with the delta effect being removed. The
worst loss of the two scenarios will be the curvature risk charge for curvature risk
factor k:
CVR 𝑘 = -min[Σi (TVChangei(RW(Curvature)+) - RW 𝑘
(Curvature) . Sik),
Σi (TVChangei(RW(Curvature)-) + RW 𝑘
(Curvature) . Sik)]
where
- i is an instrument subject to curvature risks associated with risk factor k
- RW(Curvature)+ and RW(Curvature)- are upward and downward shocks respectively
- RW 𝑘
(Curvature) is the risk weight for curvature risk factor k for instrument i
- 𝑠ik is the delta sensitivity of instrument i with respect to the delta risk factor that
corresponds to curvature risk factor k. For Tenor based riskfactors (those of IR, CR & CM), 𝑠ik is sum of
delta sensitivities to all tenors

12. SBC – Curvature Risk Charge
 The curvature risk exposure must be aggregated within each bucket using the
corresponding prescribed correlation 𝜌 𝑘l as
where ψ(CVR 𝑘 , CVRl) = 0 if CVR 𝑘 < 0 and CVRl < 0. In all other cases, ψ(CVR 𝑘 , CVRl) = 1.
 The Curvature Risk Charge for a given Risk Class (IR, CR, ..) is computed using
the corresponding prescribed correlations between each set of buckets (say b &
c): γbc
where Sb=Σ 𝑘CVR 𝑘 for all risk factors in bucket b and Sc=Σ 𝑘CVR 𝑘 in bucket c..
The function ψ(Sb , Sc) = 0 if Sb < 0 and Sc < 0. in all other cases, ψ(Sb , Sc) = 1.
If the final sum inside the square root is a negative number, the following formulae should be used to
calculate Sb and Sc
Sb = max [min(Σ 𝑘CVR 𝑘, 𝐾 𝑏), − 𝐾 𝑏]
Sc= max [min(Σ 𝑘CVR 𝑘, 𝐾c), − 𝐾c]

13. Standardized Charge – Default Risk Charge
Default Risk Charge (DRCU)
 The default risk charge is intended to capture jump-to-default-risk (JTD) of IM
unapproved Trading Desks.
 DRCU has to be computed separately for Non-Securitisations, Securitisations
(non-correlation trading portfolio) and Securitisations (Correlation Trading
Portfolio).
DRCU = DRCNon-Securitisations + DRCSecuritisations-non CTP + CSecuritisations-CTP
 The DRCU calculation involves the following steps:
 Compute Gross JTD for each instrument, exposure by exposure
 Where permissible (refer netting rules), compute net long and net short JTD losses by
obligor
 Discount net short exposures by hedge benefit ratio
 Apply default risk weights and compute capital charge

14. Default Risk Charge for Non-Securitisations
 First bucket all instruments into the following 3 categories: corporates,
sovereigns, and Muni/Local Gov.
 For each bucket, compute Gross JTD, Net JTD and then Default Risk Charge
(DRCb) using the following:
where
i refers to an instrument belonging to bucket b.
WtS is the hedge benefit discount.
RWi is default risk weight of each credit quality (rating)
 The Default Risk Charge (DRC) for Non-Securitisations is computed as simple
sum of the bucket level capital charges
DRCNon-Securitisations = DRCCorporates + DRCSovereigns + DRCMuni/LocalGov

15. DRC for Non-Securitisations – Gross JTD
Gross JTD
Gross JTD is computed exposure by exposure using the following formulae:
JTD (long) = max (LGD x Notional + P&L, 0)
JTD (short) = min (LGD x Notional + P&L, 0)
where LGD = 1 – RR(LGD: Loss Given Default, RR: Recovery Ratio)
P&L = MarketValue – Notional
The equations for JTD can be rewritten as
JTD (long) = max (MarketValue – RR x Notional, 0)
JTD (short) = min (MarketValue – RR x Notional, 0)
 For Equity instruments and non-senior debt instruments LGD = 100%, i.e., zero recovery.
 Covered bonds are assigned an LGD of 25%
 Where an institution has approved LGD estimates as part of the internal ratings based (IRB) approach, that data must
be used.

16. DRC for Non-Securitisations – Net JTD
Net JTD
Net JTD is computed using the following netting/offsetting rules
 To account for defaults within the one year capital horizon, the JTD for all exposures of
maturity less than one year and their hedges are scaled by a fraction of a year. No scaling
is applied for exposures of one year or greater.
 Cash equity positions are assigned to a maturity of either more than one year, or 3
months, at firms’ discretion
 For derivative exposures, the maturity of the derivative contract is considered
 For products with maturity < 3M, maturity weight = 0.25 (i.e., 3Months)
 The gross JTD amounts 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.
 The offsetting may result in net long JTD amounts and net short JTD amounts. The
hedge benefit discount (WtS) is computed as follows:

17. Default Risk Charge for Securitisations
(non-CTP)
 The Default Risk Charge for Securitisation (non-CTP) calculation is similar to
that of Non-Securitisations, except that the buckets are defined as follows:
 All Corporates, irrespective of region, constitute a unique bucket
 Rest are grouped into 4 regions and 11 Asset Classes as below:
Regions: Asia, Europe, North America, All other
Asset Classes: ABCP, Auto Loans/Leases, RMBS, Credit Cards, CMBS, CLO, CDO-squared,
Small and Medium Enterprises, Student loans, Other retail, Other wholesale.
DRCSecuritisations-non CTP = DRCCorporates + Σi Σj DRCi, j
where i and j stands for Region and Asset Class, respectively
 The Default Risk Charge for each bucket (DRCb) is computed similar to Non-
securitisations

18. DRC for Securitisations (non-CTP) – Gross &
Net JTD
Gross JTD
Gross JTD is computed exposure by exposure, similar to Non-Securitisation, except that JTD for
Securitisations is same as Market Value (MDE)
JTD (long) = max (MDE, 0)
JTD (short) = min (MDE, 0)
Net JTD
Netting/offsetting is limited
 No offsetting is permitted between Securitisation exposures with different underlying
Securitised portfolio (ie underlying asset pools), even if the attachment and detachment
points are the same
 No offsetting is permitted between Securitisation exposures arising from different tranches
with the same Securitised portfolio
 Securitisation exposures that are otherwise identical except for maturity may be offset
 Securitisation exposures that can be perfectly replicated through decomposition may be offset
(long vs decomposed short).
 If non-securitised instruments are used in hedging, they should be removed from non-
securitised default risk treatment

19. DRC for Securitisations (CTP)
 The DRC calculation for Correlation Trading Portfolio (CTP) is similar to that of Non-CTP,
except that each Index is treated as a bucket of its own.
 All bespoke tranches (with custom attachment-detachment points) should be allocated to the
index bucket of the index they are a bespoke tranche of.
 A deviation from the non-CTP portfolio is that no floor at 0 is made at bucket level, and as a
consequence, the default risk charge at index level (DRCb) can be negative
where
i refers to an instrument belonging to bucket b.
WtSctp is the hedge benefit ratio, computed using the combined long and short positions across the
entire CTP portfolio and not just the positions in the particular bucket
RWi is default risk weight of each tranche.
 The Default Risk Charge for CTP is computed using
where b stands for index bucket

20. DRC for Securitisations (CTP) – Gross JTD
Gross JTD
 Gross JTD calculation for securitisations in the CTP portfolio is similar to Securitisation
for non-CTP.
JTD (long) = max (MDE, 0)
JTD (short) = min (MDE, 0)
 Nth-to-default products should be treated as tranched products with attachment and
detachment points defined as:
 attachment point = (N – 1) / Total Names
 detachment point = N / Total Na
where “Total Names” is the total number of names in the underlying basket or pool

21. DRC for Securitisations (CTP) – Net JTD
Net JTD
 Securitisation exposures that are otherwise identical except for maturity may be offset, subject
to the same restriction as for positions of less than one year described previously for
Securitisations with non-CTP
 For index products, with the exact same index family (eg CDX NA IG), series (eg series 18) and
tranche (eg 0–3%), securitisation exposures should be offset (netted) across maturities
 Long/short exposures that are perfect replications through decomposition may be offset.
However, decomposition is restricted to “vanilla” securitisations (eg vanilla CDOs, index
tranches or bespokes); while the decomposition of “exotic” securitisations (eg CDO-squared) is
prohibited
 For long/short positions in index tranches, and indices (non-tranched), if the exposures are to
the exact same series of the index, then offsetting is allowed by replication and decomposition.
For instance, a long securitisation exposure in a 10–15% tranche vs combined short
securitisation exposures in 10–12% and 12–15% tranches on the same index/series can be offset
against each other
 Long/short positions in indices and single-name constituents in the index may also be offset by
decomposition.

22. Standardized Charge – Residual Risk Add-
On
Residual Risk Add-On
 Residual Risk Add-On captures any other risks beyond the main risk factors already captured in the
sensitivities-based method or DRC. It provides for a simple and conservative capital treatment for the
more sophisticated/complex instruments that would otherwise not be captured in a practical manner
under the other two components of the revised standardised approach
 The residual risk add-on is the simple sum of gross notional amounts of the instruments bearing
residual risks, multiplied by a risk weight of 1.0% for instruments with an exotic underlying and a risk
weight of 0.1% for instruments bearing other residual risks
 The following criteria can be used to identify instruments for which Residual Risk Add-On should be
computed
 instruments subject to vega or curvature risk capital charges in the trading book and with pay-offs that cannot be
written or perfectly replicated as a finite linear combination of vanilla options with a single underlying equity
price, commodity price, exchange rate, bond price, CDS price or interest rate swap
 Gap risk: risk of a significant change in vega parameters in options due to small movements in the underlying,
which results in hedge slippage. Relevant instruments subject to gap risk include all path dependent options,
such as barrier options, and Asian options, as well as all digital options
 Correlation risk: risk of a change in a correlation parameter necessary for determination of the value of an
instrument with multiple underlyings. Relevant instruments subject to correlation risk include all basket options,
best-of-options, spread options, basis options, Bermudan options and quanto options
 Behavioural risk: risk of a change in exercise/prepayment outcomes such as those that arise in fixed rate
mortgage products where retail clients may make decisions motivated by factors other than pure financial gain

23. Internal Models Approach – Expected
Shortfall (ES)
Expected Shortfall (ES)
 The existing measures: VaR and SVaR (Stressed VaR) will be replaced with one single
measure: Expected Shortfall (ES)
 Expected Shortfall calculation will be based on a 1-year stress period in which portfolio
experiences the largest loss. The observation horizon for determining the most stressful
12 months must span from 2007. Banks must update their 12-month stressed
periods no less than monthly, or whenever there are material changes in the portfolio.
 All Risk factors are bucketed into
Risk factor categories and each Risk factor
category is mapped to a Liquidity horizon
as shown in the table

24. Internal Models Approach – Expected
Shortfall (ES)
 Aggregate Hypothetical PnL Vectors and compute Expected Shortfall EST(P, j) at horizon T (=10), as
average of 97.5th percentile tail, for risk factors Q(pi , j) in such a way that the liquidity horizons of the
risk factors are at least as long as LHj (>= LHj)
 Compute Expected Shortfall for each risk factor class (Total(All Rfs), IR, CR, FX, EQ & CM) using the
following formula
where
 ES is the regulatory liquidity-adjusted expected shortfall
 T is the length of the base horizon, i.e., 10 days
 EST(P) is the expected shortfall at horizon T of a portfolio with positions P = (pi) with respect to shocks to all
risk factors that the positions P are exposed to;
 LHj is the liquidity horizon (10, 20, 40, 60, 120), so j = 1->5
 EST(P, j) is the expected shortfall at horizon T of a portfolio with positions P = (pi) with respect to shocks for
each position pi in the subset of risk factors Q(pi , j), whose Liquidity horizon >= LHj
 Q(pi , j) j is the subset of risk factors whose liquidity horizons for the desk where pi is booked are at least as
long as LHj

25. Internal Models Approach – Stressed
Capital Add-On (SES)
Stressed Capital Add-On (SES)
This charge is for non-modellable risk factors in model-eligible desks.
 Each non-modellable risk factor is to be capitalised using a stress scenario that is calibrated to be at
least as prudent as the expected shortfall calibration used for modelled risks (ie a loss calibrated to a
97.5% confidence threshold over a period of extreme stress for the given risk factor).
 For each non-modellable risk factor, the liquidity horizon of the stress scenario must be the greater of
the largest time interval between two consecutive price observations over the prior year
 No correlation or diversification effect between other non-modellable risk factors is permitted.
 The aggregate regulatory capital measure for L (non-modellable idiosyncratic credit spread risk
factors that have been demonstrated to be appropriate to aggregate with zero correlation) and K (risk
factors in model-eligible desks that are non-modellable (SES)) is:
where ISESNM, i is the stress scenario capital charge for idiosyncratic credit spread non-
modellable risk i from the L risk factors aggregated with zero correlation; and SESNM, j is the stress
scenario capital charge for non-modellable risk j.

26. IT Infrastructure Challenges
 Many banks built different systems to compute VaR, IRC, CRM, etc, but FRTB
provides an opportunity to consolidate various calculations in one platform
 Good news is that most of the FRTB calculations can be performed using the
same feeds/inputs that are used in VaR and IRC
 Normalization of riskfactor attributes to match FRTB requirements
 Frequent calibration of Stress Period might put additional burden on IT
infrastructure
 Additional compute capacity to support:
 Computation of both SA and IMA charges on a daily basis so that business
can manage capital using both SA and IMA approaches
 What-if analysis capabilities: With so many charges going into Capital
Charge calculation, a revamp of reporting and tools that provide
transparency into various charges is needed

27. Appendix

28. Sensitivities Charge – GIRR Delta Risk
Weights & Correlations
Buckets: bucketed by Curve Currency
Risk Weights
 Risk Weights are based on Tenor (Vertex) as shown in table
 For Inflation and Cross Currency basis risk factors, Risk Weight is 2.25%
 For selected currencies (EUR, USD, GBP, AUD, JPY, SEK, CAD and domestic reporting currency of a bank), the risk
weights in the above table may, at the discretion of the bank, be divided by the square root of 2
Correlations
 For a given bucket, the delta risk correlation (𝜌 𝑘l) is set at 99.90% between sensitivities with same Tenor but different
curves
 For a given bucket and Curve, the delta risk correlation (𝜌 𝑘l) between different Tenors is set at
where 𝑇 𝑘 (respectively 𝑇l) is the vertex that relates to WS 𝑘 (respectively WSl) and 𝜃 set at 3%.
 Between two sensitivities WS 𝑘 and WSl within the same bucket, different vertex and different curves, the correlation 𝜌 𝑘l
is equal to the product of 99.9% and
 The delta risk correlation 𝜌 𝑘l between a sensitivity WS 𝑘 to the inflation curve and a sensitivity WSl to a given vertex of
the relevant yield curve is 40%.
 The delta risk correlation 𝜌 𝑘l between a sensitivity WS 𝑘 to a cross currency basis curve and a sensitivity WSl to either a
given vertex of the relevant yield curve, the inflation curve or another cross currency basis curve (if relevant) is 0%
 The parameter γbc = 50% must be used for aggregating between different buckets (currencies)

29. Sensitivities Charge – Delta CSR Non-
Securitisations Risk Weights & Correlations
Buckets: bucketed by Sector and Credit Quality (as shown in the table below)
Risk Weights
 The risk weights for the buckets 1 to 16 are set out in the following table. Risk weights are the same for all vertices (ie
0.5 year, 1 year, 3 year, 5 year, 10 year) within each bucket

30. Sensitivities Charge – Delta CSR Non-
Securitisations Risk Weights & Correlations
Correlations
 Between two sensitivities WS 𝑘 and WSl within the same bucket, the correlation parameter 𝜌 𝑘l is set as follows
where
 𝜌 𝑘l
(name) is equal to 1 where the two names of sensitivities k and l are identical, and 35% otherwise
 𝜌 𝑘l
(tenor) is equal to 1 if the two vertices of the sensitivities k and l are identical, and to 65% otherwise
 𝜌 𝑘l
(basis) is equal to 1 if the two sensitivities are related to same curves, and 99.90% otherwise
 The above correlation calculation is not applicable to Curvature Risk context
 The above correlation calculation is also not applicable to "other sector" bucket. The “other sector” bucket capital
requirement for the delta and vega risk aggregation formula would be equal to the simple sum of the absolute values of
the net weighted sensitivities allocated to this bucket. This “other sector” bucket level capital will be added to the
overall risk class level capital, with no diversification or hedging effects recognized with any bucket
 The correlation parameter γbc is set as follows
 γbc
(rating) is equal to 1 where the two buckets b and c have the same rating category (either IG or
HY/NR), and 50% otherwise
 γbc
(sector) is equal to 1 if the two buckets have the same sector,
and to the following numbers otherwise:

31. Sensitivities Charge – Delta CSR
Securitisations (CTP) Risk Weights &
Correlations
Buckets: bucketed by Sector and Credit Quality. The bucket classification is same as Non-Securitisations (ref Non-
Securitisations table)
Risk Weights
 Risk Weights for Securitisations (non-CTP) are different to reflect longer liquidity horizons and larger basis risk. Risk
weights are the same for all vertices (ie 0.5 year, 1 year, 3 year, 5 year, 10 year) within each bucket
Correlations
 Within bucket correlations (𝜌 𝑘l) are calculated same way as Non-Securitisations except that 𝜌 𝑘l
(basis) is now equal to 1 if
the two sensitivities are related to same curves, and 99.00% otherwise.
 Bucket Correlations (γbc) are same as Non-Securitisations

32. Sensitivities Charge – Delta CSR
Securitisations (non-CTP) Risk Weights &
Correlations
Buckets: bucketed by Sector and Credit Quality (as shown in the table below). Banks must assign each tranche to one of
the sector buckets in the table
Risk Weights
 The risk weights for the buckets 1 to 8 (Senior-IG) are set out in the following table.
 The risk weights for the buckets 9 to 16 (Non-Senior IG) are equal to the corresponding risk weights for the buckets 1 to
8 scaled up by a multiplication by 1.25
 The risk weights for the buckets 17 to 24 (High yield & non-rated) are equal to the corresponding risk weights for the
buckets 1 to 8 scaled up by a multiplication by 1.75
 The risk weight for bucket 25 is set at 3.5%.

33. Sensitivities Charge – Delta CSR
Securitisations (non-CTP) Risk Weights &
Correlations
Correlations
 Between two sensitivities WS 𝑘 and WSl within the same bucket, the correlation parameter 𝜌 𝑘l is set as follows
where
 𝜌 𝑘l
(tranche) is equal to 1 where the two names of sensitivities k and l are within the same bucket and related to the same securitisation
tranche (more than 80% overlap in notional terms), and 40% otherwise
 𝜌 𝑘l
(tenor) is equal to 1 if the two vertices of the sensitivities k and l are identical, and to 80% otherwise
 𝜌 𝑘l
(basis) is equal to 1 if the two sensitivities are related to same curves, and 99.90% otherwise
 The above correlation calculation is also not applicable to "other sector" bucket. The “other sector” bucket capital
requirement for the delta and vega risk aggregation formula would be equal to the simple sum of the absolute values of
the net weighted sensitivities allocated to this bucket. This “other sector” bucket level capital will be added to the
overall risk class level capital, with no diversification or hedging effects recognized with any bucket
 The correlation between different buckets (γbc) is set as 0%

34. Sensitivities Charge – Equity Delta Risk
Weights & Correlations
Buckets: bucketed by Economy, Sector and Market Cap.
 Large Market Cap: Market Capitialization >= $2 billion, otherwise Small Cap
 The advanced economies are Canada, the United States, Mexico, the euro area, the non-euro area western European
countries (the United Kingdom, Norway, Sweden, Denmark and Switzerland), Japan, Oceania (Australia and New
Zealand), Singapore and Hong Kong SAR

35. Sensitivities Charge – Equity Delta Risk
Weights & Correlations
Risk Weights: The risk weights for the sensitivities to Equity spot price and Equity repo rate for buckets 1 to 11 are set out
in the following table

36. Sensitivities Charge – Equity Delta Risk
Weights & Correlations
Correlations
 The delta risk correlation parameter 𝜌 𝑘l set at 99.90% between two sensitivities WS 𝑘 and WSl within the same bucket where one is a
sensitivity to an Equity spot price and the other a sensitivity to an Equity repo rate, where both are related to the same Equity issuer name
 The correlation parameter 𝜌 𝑘l between two sensitivities WS 𝑘 and WSl , either both to Equity spot price or to Equity Report Rate, within the
same bucket are defined
1. 15% between two sensitivities within the same bucket that fall under large market cap, emerging market economy (bucket number 1, 2,
3 or 4).
2. 25% between two sensitivities within the same bucket that fall under large market cap, advanced economy (bucket number 5, 6, 7, or
8).
3. 7.5% between two sensitivities within the same bucket that fall under small market cap, emerging market economy (bucket number
9).
4. 12.5% between two sensitivities within the same bucket that fall under small market cap, advanced economy (bucket number 10).
 Between two sensitivities WS 𝑘 and WSl within the same bucket where one is a sensitivity to an Equity spot price and the other a sensitivity to
an Equity repo rate and both sensitivities relate to a different Equity issuer name, the correlation parameter 𝜌 𝑘l is set at the correlations
specified above (4 bullet points) multiplied by 99.90%.
 The above correlations are not applicable to "other sector" bucket. The “other sector” bucket capital requirement for the delta and vega risk
aggregation formula would be equal to the simple sum of the absolute values of the net weighted sensitivities allocated to this bucket. This
“other sector” bucket level capital will be added to the overall risk class level capital, with no diversification or hedging effects recognized
with any bucket
 The correlation between different buckets (γbc) is set as 15% if both buckets fall within bucket numbers 1 to 10

37. Sensitivities Charge – Commodity Delta
Risk Weights & Correlations
Buckets & Risk Weights: bucketed by grouping commodities with similar characteristics

38. Sensitivities Charge – Commodity Delta
Risk Weights & Correlations
Correlations
 Between two sensitivities WS 𝑘 and WSl within the same bucket, the correlation parameter 𝜌 𝑘l is set as follows
where
 𝜌 𝑘l
(cty) is equal to 1 where the two commodities of sensitivities k and l are identical, and to the intra-bucket correlations in the table
below otherwise
 𝜌 𝑘l
(tenor) is equal to 1 if the two vertices of the sensitivities k and l are identical, and to 99% otherwise
 𝜌 𝑘l
(basis) is equal to 1 if the two sensitivities are identical in both (i) contract grade of the commodity, and (ii) delivery location of a
commodity, and 99.90% otherwise
 The correlation between different buckets (γbc) is set as 20% if both buckets fall within bucket numbers 1 to 10 and set
to 0% if either one of the bucket is 11.

39. Sensitivities Charge – FX Delta Risk Weights
& Correlations
Buckets : Each Currency pair is treated as a bucket
Risk Weights
 A unique relative risk weight equal to 30% applies to all the FX sensitivities
 For the specified currency pairs (USD/EUR, USD/JPY, USD/GBP, USD/AUD, USD/CAD, USD/CHF, USD/MXN,
USD/CNY, USD/NZD, USD/RUB, USD/HKD, USD/SGD, USD/TRY, USD/KRW, USD/SEK, USD/ZAR, USD/INR,
USD/NOK, USD/BRL, EUR/JPY, EUR/GBP, EUR/CHF and JPY/AUD) by the Basel Committee, the above risk
weight may at the discretion of the bank be divided by the square root of 2
Correlations
 A uniform correlation parameter γbc equal to 60% is applied to all Currency pair buckets

40. Sensitivities Charge – Vega Risk Weights &
Correlations
Buckets : Vega buckets are same as corresponding Delta buckets for a given Risk Class
Risk Weights
 The Vega risk weight for a given risk factor is computed by using the following formula. The risk of market illiquidity is
incorporated into Vega Risk weights by scaling with appropriate liquidity horizons
Where
 𝑅 𝜎 is set at 55%;
 𝐿Hrisk class is the liquidity horizon for a given risk class shown in the table below

41. Sensitivities Charge – Vega Risk Weights &
CorrelationsCorrelations for GIRR
 Between vega risk sensitivities within the same bucket of the GIRR risk class, the correlation parameter 𝜌 𝑘l is set as follows
where
 𝜌 𝑘l
(option maturity) is equal to where 𝛼 is set at 1%, 𝑇 𝑘 (respectively 𝑇l) is the maturity of the option from which the
vega sensitivity VR 𝑘(VRl) is derived, expressed as a number of years;
 𝜌 𝑘l
(underlying maturity) is equal to where 𝛼 is set at 1%, 𝑇 𝑘
U (respectively 𝑇l
U) is the maturity of the underlying of the
option from which the sensitivity VR 𝑘(VRl) is derived, expressed as a number of years after the maturity of the option.
Correlations for FX, EQ, CR & CM
 Between vega risk sensitivities within a bucket of the other risk classes (ie not GIRR), the correlation parameter 𝜌 𝑘l is set as
follows
where
 𝜌 𝑘l
(DELTA) is equal to the correlation that applies between the delta risk factors that correspond to vega risk factors k and l,
i.e., use same correlations as those used in Delta
 𝜌 𝑘l
(option maturity) is equal to where 𝛼 is set at 1%, 𝑇 𝑘 (respectively 𝑇l) is the maturity of the option from which the
vega sensitivity VR 𝑘(VRl) is derived, expressed as a number of years;
Correlations between buckets
 For all risk classes, use same correlations as those used for Delta sensitivities

42. Sensitivities Charge – Curvature Risk
Weights & Correlations
Buckets : Curvature buckets are same as corresponding Delta buckets for a given Risk Class
Risk Weights
 For FX and EQ curvature risk factors, the curvature risk weights are relative shifts (“shocks”) equal to the delta risk
weights
 For GIRR, CSR and Commodity curvature risk factors, the curvature risk weight is the parallel shift of all the vertices
for each curve based on the highest prescribed delta risk weight for each risk class. For example, in the case of GIRR the
risk weight assigned to the 0.25 year vertex (ie most punitive vertex risk weight) is applied to all the vertices
simultaneously for each risk-free yield curve
Correlations
 Between curvature exposures, each delta correlation parameters 𝜌 𝑘l and γbc should be squared. For instance, between 𝐶
VR 𝐸UR and 𝐶VRUSD in the GIRR context, the correlation should be 50%2 =25%.

43. Acknowledgements
Most of the content is sourced from BCBS – Minimum Capital Requirement for Market Risk
specification