FRTB Capital Charge
FRTB Capital Charge CalculationRamesh Jonnadula
FRTB Overview of Key Rules/ChangesMore Granular Model Approval
ProcessInternal Model Approvals/revocation will be done at Trading
Desk level as compared to current Bank level IMA approvalsIMA
eligible desks will be subjected to new P&L attribution tests
in addition to Back-testingOverhaul of IMAReplace 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 windowCapture of
liquidity riskLiquidity is defined at risk factor level, not
position levelLiquidity horizons are prescribed by FRTB: 10, 20,
40, 60, 120Constraints 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 RiskAbandon CRM in favor of Standardized
Charge
FRTB Market Risk Capital Charge Components
Basel 2.5 vs FRTBBasel 2.5FRTBIMA ApproachVaRExpected Shortfall
(ES)Stressed VaRIncremental Risk Charge (IRC)Default Risk Charge
(DRC)RNiV by some regulatorsStress Capital Addon (NMRF)ORAND
Standardized ApproachStandardized ChargeCRMSensitivity based
ChargeDefault Risk Charge (DRC)NoneResidual Risk Addon
Capital Charge
Aggregate Capital ChargeThe 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)
Capital Charge for Standardized Approach
Aggregate Capital Charge for Standardized ApproachThe Aggregate
Standardized Capital Charge for unapproved Trading desks
Standardized Charge (CU) = Sensitivities based Charge + Residual
Risk Add-on
Capital Charge for IMA
Capital Charge for Internal Model ApproachThe aggregated charge
associated with approved desks (C) 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 = max( (IMCCt-1 + SESt-1) , (mc . IMCC60DayAvg + SES60DayAvg)
)
whereIMCC is Capital Charge for Modellable riskfactors of IM
approved desksSES is Stressed Capital Addon for Non-Modellable risk
factors of IM Approved Trading DesksThe multiplication factor mc
>= 1.5 and will be set by individual supervisory authorities on
the basis of their assessment of the quality of the banks risk
management system
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 = . ESunconstrained + (1- ) .
ESconstrainedwhereESunconstrained = ESTotal(AllRfs) (ES for all
Risk factors honoring diversification)ESconstrained = ESIR + ESCR +
ESEQ + ESFX + ESCM (Sum of individual ES for all risk classes) is
the relative weight assigned to the firm's internal model, which is
currently set as 0.5.
Standardized Charge Sensitivities based ChargeSensitivities
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 isDelta 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)
SBC Delta & Vega Risk ChargesDelta & Vega Risk
ChargesCalculate net sensitivity across instruments to each risk
factor k (decompose ndex instruments and multi-underlying options).
Assign Risk weights (R) to each Riskfactor and compute weighted
sensitivity S asGroup the Riskfactors in a given Risk Class into
buckets. The risk position for Delta bucket b (respectively Vega),
, computed using correlation between riskfactors (l) using the
following formula:
If the value inside the square root is ve, = 0The Delta
(respectively Vega) risk charge for a given Risk Class (IR, CR, ..)
is computed using bucket correlations (bc):
where Sb=S for all risk factors in bucket b and Sc=S in bucket
c.. If the value inside square root is ve, use the following Sb =
max [min(S, ), ] Sc= max [min(S, c), c]
SBC Curvature Risk ChargeCurvature Risk ChargeCurvature 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 = -min[i
(TVChangei(RW(Curvature)+) - RW(Curvature) . Sik), i
(TVChangei(RW(Curvature)-) + RW(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(Curvature) is the risk weight for curvature risk
factor k for instrument i - ik 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), ik is sum of delta sensitivities to all
tenors
SBC Curvature Risk ChargeThe curvature risk exposure must be
aggregated within each bucket using the corresponding prescribed
correlation l as
where (CVR , CVRl) = 0 if CVR < 0 and CVRl < 0. In all
other cases, (CVR , 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): bc
where Sb=CVR for all risk factors in bucket b and Sc=CVR in
bucket c..The function (Sb , Sc) = 0 if Sb < 0 and Sc < 0. in
all other cases, (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(CVR, ), ]Sc= max [min(CVR, c),
c]
Standardized Charge Default Risk ChargeDefault 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 exposureWhere permissible
(refer netting rules), compute net long and net short JTD losses by
obligorDiscount net short exposures by hedge benefit ratioApply
default risk weights and compute capital charge
Default Risk Charge for Non-SecuritisationsFirst 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:
wherei 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
chargesDRCNon-Securitisations = DRCCorporates + DRCSovereigns +
DRCMuni/LocalGov
DRC for Non-Securitisations Gross JTDGross JTDGross 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)
whereLGD = 1 RR(LGD: Loss Given Default, RR: Recovery
Ratio)P&L = MarketValue Notional
The equations for JTD can be rewritten asJTD (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.
DRC for Non-Securitisations Net JTDNet JTDNet JTD is computed
using the following netting/offsetting rulesTo 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 discretionFor
derivative exposures, the maturity of the derivative contract is
consideredFor 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:
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
bucketRest are grouped into 4 regions and 11 Asset Classes as
below:Regions: Asia, Europe, North America, All otherAsset 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 + i j 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
DRC for Securitisations (non-CTP) Gross & Net JTDGross
JTDGross 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 JTDNetting/offsetting is limitedNo offsetting is permitted
between Securitisation exposures with different underlying
Securitised portfolio (ie underlying asset pools), even if the
attachment and detachment points are the sameNo offsetting is
permitted between Securitisation exposures arising from different
tranches with the same Securitised portfolioSecuritisation
exposures that are otherwise identical except for maturity may be
offsetSecuritisation 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
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
wherei 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
DRC for Securitisations (CTP) Gross JTDGross JTDGross 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
DRC for Securitisations (CTP) Net JTDNet JTDSecuritisation
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-CTPFor index products, with the exact same index family (eg CDX
NA IG), series (eg series 18) and tranche (eg 03%), securitisation
exposures should be offset (netted) across maturitiesLong/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
1015% tranche vs combined short securitisation exposures in 1012%
and 1215% tranches on the same index/series can be offset against
each otherLong/short positions in indices and single-name
constituents in the index may also be offset by decomposition.
Standardized Charge Residual Risk Add-OnResidual Risk
Add-OnResidual 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 approachThe 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 risksThe following
criteria can be used to identify instruments for which Residual
Risk Add-On should be computedinstruments 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 swapGap 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
optionsCorrelation 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
optionsBehavioural 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
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 intoRisk
factor categories and each Risk factorcategory is mapped to a
Liquidity horizonas shown in the table
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
whereES is the regulatory liquidity-adjusted expected shortfallT
is the length of the base horizon, i.e., 10 daysEST(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->5EST(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
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
yearNo 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.
IT Infrastructure ChallengesMany banks built different systems
to compute VaR, IRC, CRM, etc, but FRTB provides an opportunity to
consolidate various calculations in one platformGood 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 requirementsFrequent
calibration of Stress Period might put additional burden on IT
infrastructureAdditional 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 approachesWhat-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
Appendix
Sensitivities Charge GIRR Delta Risk Weights &
CorrelationsBuckets: bucketed by Curve CurrencyRisk WeightsRisk
Weights are based on Tenor (Vertex) as shown in tableFor 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 CorrelationsFor a given bucket, the delta risk correlation (l)
is set at 99.90% between sensitivities with same Tenor but
different curvesFor a given bucket and Curve, the delta risk
correlation (l) between different Tenors is set at where
(respectively l) is the vertex that relates to WS (respectively
WSl) and set at 3%. Between two sensitivities WS and WSl within the
same bucket, different vertex and different curves, the correlation
l is equal to the product of 99.9% and
The delta risk correlation l between a sensitivity WS to the
inflation curve and a sensitivity WSl to a given vertex of the
relevant yield curve is 40%.The delta risk correlation l between a
sensitivity WS 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 bc = 50% must be used for aggregating between
different buckets (currencies)
Sensitivities Charge Delta CSR Non-Securitisations Risk Weights
& CorrelationsBuckets: bucketed by Sector and Credit Quality
(as shown in the table below)Risk WeightsThe 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
Sensitivities Charge Delta CSR Non-Securitisations Risk Weights
& CorrelationsCorrelationsBetween two sensitivities WS and WSl
within the same bucket, the correlation parameter l is set as
follows
wherel (name) is equal to 1 where the two names of sensitivities
k and l are identical, and 35% otherwise l (tenor) is equal to 1 if
the two vertices of the sensitivities k and l are identical, and to
65% otherwisel (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 contextThe 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 bc is set as followsbc(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 bc(sector) is
equal to 1 if the two buckets have the same sector, and to the
following numbers otherwise:
Sensitivities Charge Delta CSR Securitisations (CTP) Risk
Weights & CorrelationsBuckets: bucketed by Sector and Credit
Quality. The bucket classification is same as Non-Securitisations
(ref Non-Securitisations table)
Risk WeightsRisk 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
CorrelationsWithin bucket correlations (l) are calculated same
way as Non-Securitisations except that l (basis) is now equal to 1
if the two sensitivities are related to same curves, and 99.00%
otherwise.Bucket Correlations (bc) are same as
Non-Securitisations
Sensitivities Charge Delta CSR Securitisations (non-CTP) Risk
Weights & CorrelationsBuckets: 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 WeightsThe 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
1.25The 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%.
Sensitivities Charge Delta CSR Securitisations (non-CTP) Risk
Weights & CorrelationsCorrelationsBetween two sensitivities WS
and WSl within the same bucket, the correlation parameter l is set
as follows
wherel (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 l (tenor) is equal to 1 if the two
vertices of the sensitivities k and l are identical, and to 80%
otherwisel (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 (bc) is set as 0%
Sensitivities Charge Equity Delta Risk Weights &
CorrelationsBuckets: bucketed by Economy, Sector and Market
Cap.
Large Market Cap: Market Capitialization >= $2 billion,
otherwise Small CapThe 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
Sensitivities Charge Equity Delta Risk Weights &
CorrelationsRisk 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
Sensitivities Charge Equity Delta Risk Weights &
CorrelationsCorrelationsThe delta risk correlation parameter l set
at 99.90% between two sensitivities WS 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 nameThe correlation parameter l between
two sensitivities WS and WSl , either both to Equity spot price or
to Equity Report Rate, within the same bucket are defined15%
between two sensitivities within the same bucket that fall under
large market cap, emerging market economy (bucket number 1, 2, 3 or
4).25% between two sensitivities within the same bucket that fall
under large market cap, advanced economy (bucket number 5, 6, 7, or
8). 7.5% between two sensitivities within the same bucket that fall
under small market cap, emerging market economy (bucket number 9).
12.5% between two sensitivities within the same bucket that fall
under small market cap, advanced economy (bucket number 10).
Between two sensitivities WS 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 l 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 (bc) is set as 15% if
both buckets fall within bucket numbers 1 to 10
Sensitivities Charge Commodity Delta Risk Weights &
CorrelationsBuckets & Risk Weights: bucketed by grouping
commodities with similar characteristics
Sensitivities Charge Commodity Delta Risk Weights &
CorrelationsCorrelationsBetween two sensitivities WS and WSl within
the same bucket, the correlation parameter l is set as follows
wherel (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 l (tenor) is equal to 1
if the two vertices of the sensitivities k and l are identical, and
to 99% otherwisel (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 (bc) 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.
Sensitivities Charge FX Delta Risk Weights &
CorrelationsBuckets : Each Currency pair is treated as a bucketRisk
WeightsA unique relative risk weight equal to 30% applies to all
the FX sensitivitiesFor 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
CorrelationsA uniform correlation parameter bc equal to 60% is
applied to all Currency pair buckets
Sensitivities Charge Vega Risk Weights & CorrelationsBuckets
: Vega buckets are same as corresponding Delta buckets for a given
Risk ClassRisk WeightsThe 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 is set at 55%; Hrisk class is the liquidity horizon for a
given risk class shown in the table below
Sensitivities Charge Vega Risk Weights &
CorrelationsCorrelations for GIRRBetween vega risk sensitivities
within the same bucket of the GIRR risk class, the correlation
parameter l is set as follows
wherel (option maturity) is equal to where is set at 1%,
(respectively l) is the maturity of the option from which the vega
sensitivity VR(VRl) is derived, expressed as a number of years;
l (underlying maturity) is equal to where is set at 1%, U
(respectively lU) is the maturity of the underlying of the option
from which the sensitivity VR(VRl) is derived, expressed as a
number of years after the maturity of the option. Correlations for
FX, EQ, CR & CMBetween vega risk sensitivities within a bucket
of the other risk classes (ie not GIRR), the correlation parameter
l is set as follows
wherel (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
l (option maturity) is equal to where is set at 1%,
(respectively l) is the maturity of the option from which the vega
sensitivity VR(VRl) is derived, expressed as a number of
years;Correlations between bucketsFor all risk classes, use same
correlations as those used for Delta sensitivities
Sensitivities Charge Curvature Risk Weights &
CorrelationsBuckets : Curvature buckets are same as corresponding
Delta buckets for a given Risk Class
Risk WeightsFor 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
CorrelationsBetween curvature exposures, each delta correlation
parameters l and bc should be squared. For instance, between VRUR
and VRUSD in the GIRR context, the correlation should be 50%2
=25%.
AcknowledgementsMost of the content is sourced from BCBS Minimum
Capital Requirement for Market Risk specification
