FRTB Overview of Key Rules Changes

FRTB – Overview of Key Rules/Changes
 All global systematically important banks or those involved in correlation trading are required to choose between
Standardised approach (SA) and Internal Models Approach (IMA)
 All banks must calculate the capital requirements using the standardised approach.
 A bank that uses the IMA for any of its trading desks must calculate the standardised approach capital requirement for
each trading desk that is eligible for the IMA as a fallback mechanism
 Internal Model Approvals/revocation will be done at Trading Desk level as compared to current Bank level IMA
approvals
IMA Eligibility Criteria
 A bank that intends to use the internal models approach (IMA) to determine market risk capital requirements for a
trading desk must conduct and successfully pass backtesting at the bank-wide level and both the backtesting and profit
and loss (P&L) attribution (PLA) test at the trading desk level
 For a bank to remain eligible to use the IMA, a minimum of 10% of the bank’s aggregated market risk capital
requirement must be based on positions held in trading desks that qualify for IMA
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 Standardised Charge
 All risk factors that are used in IMA must pass risk factor eligibility test (RFET) else they will be part of NMRF charge

FRTB Market Risk Capital Charge
Components

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)
Stress Capital Addon
(NMRF)
CVA VaR & CVA SVaR Removed
OR AND
Standardised
Approach
Standardised Charge
Sensitivity based Charge
Default Risk Charge
(DRC)
Residual Risk Addon
SA – CVA or BA - CVA

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 + CU
where
CA = Capital Charge for Internal Model Approved Trading Desks
CU = Aggregate Standardised Capital Charge for Unapproved Trading Desks

Capital Charge for Standardised Approach
Aggregate Capital Charge for Standardised Approach
The Aggregate Standardised Capital Charge for unapproved Trading desks
Standardised Charge (CU) = Sensitivities based Charge
+ Default Risk Charge (DRCU)
+ Residual Risk Add-on (RRAO)

Capital Charge for IMA
CapitalCharge 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) plus
Default Risk Charge computed using internal model (VaR model):
C 𝐴 = max( (IMCCt-1 + SESt-1) , (mc . IMCC60DayAvg + SES60DayAvg) ) + DRCA
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
DRCA = max( DRCCurrentWeek , DRC12WeekAvg)
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

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.

Standardised 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))
Under the “Medium Correlations” scenario, the correlation parameters 𝜌kl and 𝛾bc as specified in Appendix apply. Under
the “High Correlations” scenario, the correlation parameters 𝜌kl and 𝛾bc used in Medium Correlation are uniformly
multiplied by 1.25, with 𝜌kl and 𝛾bc subject to a cap at 100%. Under the “low correlations” scenario, the correlation
parameters 𝜌kl and 𝛾bc that are specified in “Medium Correlation” scenario are replaced by 𝜌kl = max(2 × 𝜌kl − 100%; 75%
× 𝜌kl) and 𝛾bc = max(2 × 𝛾bc − 100%; 75% × 𝛾bc).
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)

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]

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:
where
- i is an instrument subject to curvature risks associated with risk factor k
- x 𝑘 is the current level of risk factor k
- 𝑉𝑖(x 𝑘) is the price of instrument i at the current level of risk factor k
- and denote the price of instrument i after x 𝑘 is shifted upward and downward
respectively
- RW(Curvature)+ and RW(Curvature)- are upward and downward shocks respectively
- is same as TVChange when upward shock is applied
- 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

SBC – Curvature Risk Charge
 The curvature risk exposure must be aggregated within each bucket using the corresponding
prescribed correlation 𝜌 𝑘l. Then the bucket level capital charge (Kb)is calculated as the greater of the
capital requirement under the upward scenario (Kb
+) and the downward scenario (Kb
-)
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, when the upward scenario has been selected and
Sb=Σ 𝑘CVR 𝑘
- otherwise. Similarly, Sc is calculated for 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]

Standardised 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 (Migration Risk is already captured as part of Credit
Spread SBM)
 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

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.
HBR is the hedge benefit ratio.
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

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 = Bond-equivalent MarketValue – Notional
 A long exposure is defined as a credit exposure that results in a loss in the case of a default. For derivative contracts, the
long/short direction is also determined by whether the contract will result in a loss in the case of a default (ie long or
short position is not determined by whether the option or credit default swap (CDS), is bought or sold).
 For Equity instruments and non-senior debt instruments LGD = 100%, i.e., zero recovery.
 Senior debt instruments are assigned an LGD of 75%.
 Covered bonds are assigned an LGD of 25%
 When the price of the instrument is not linked to the recovery rate of the defaulter (eg a foreign exchange-credit hybrid
option where the cash flows are swap of cash flows, long EUR coupons and short USD coupons with a knockout
feature that ends cash flows on an event of default of a particular
 obligor), there should be no multiplication of the notional by the LGD.
 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 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 ratio (HBR) 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 bucket
 Rest are grouped into 4 regions and 11 Asset Classes as below:
Regions: Asia, Europe, North America & All other
Asset Classes: Asset-backed commercial paper, 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, i.e., by using Risk Weights, net JTD and HBR
 The default risk weights for securitisation exposures are based on the
corresponding risk weights for banking book instruments

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 (LGD is already included in the default risk weights for
securitisations to be applied)
JTD (long) = max (MarketValue, 0)
JTD (short) = min (MarketValue, 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 using similar
offsetting and scaling rules that are used in non-securitized products
 Securitisation exposures that can be perfectly replicated through decomposition may be offset (long
vs decomposed short).
 The hedge benefit discount HBR, calculated similar to non-securitized products, is applied to net
short securitisation exposures in that bucket
 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
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

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 Names
where “Total Names” is the total number of names in the underlying basket or pool

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.

Standardised Charge – Residual Risk Add-
On (RRAO)
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 with an exotic underlying. Examples include: longevity risk, weather, natural disasters, future realised volatility (as an
underlying exposure for a swap).
 Instruments which fall under the definition of the correlation trading portfolio (CTP)
 Instruments that are subjected to one or more of the following risk types: Risk from cheapest to deliver option, Dividend risk arising
from a derivative instrument whose underlying does not consist solely of dividend payments, Correlation risk arising from multi-
underlying European or American plain vanilla options,
 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

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

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. Same Stress period should be used for all Risk factor classes.
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

Internal Models Approach – Default Risk
Charge (DRC)
Default Risk Charge (DRC)
Default risk is the risk of direct loss due to an obligor’s default as well as the potential for indirect losses
that may arise from a default event. DRC under IMA must be measured using a value-at-risk (VaR) model
 Banks must use a default simulation model with two types of systematic risk factors.
 Default correlations must be based on credit spreads or on listed equity prices. Correlations must be
based on data covering a period of 10 years that includes a period of stress as calibrated for ES and
based on a one-year liquidity horizon.
 Banks must have clear policies and procedures that describe the correlation calibration process,
documenting in particular in which cases credit spreads or equity prices are used.
 Banks have the discretion to apply a minimum liquidity horizon of 60 days to the determination of
default risk capital (DRC) requirement for equity sub-portfolios.
 The VaR calculation must be conducted weekly and be based on a one-year time horizon at a one-tail,
99.9 percentile confidence level.
 All positions subject to market risk capital requirements that have default risk, with the exception of
those positions subject to the standardised approach, are subject to the DRC requirement model.
 Sovereign exposures, equity positions and defaulted debt positions must be included in the model.
 For equity positions, the default of an issuer must be modelled as resulting in the equity price
dropping to zero.

Risk Factor model Eligibility Test (RFET)
Only the risk factors that pass Risk Factor Eligibility Test (RFET) are eligible to be included in the bank’s
internal model, else those risk factors should be included in the SES (NMRF) charge. This test requires
identification of a sufficient number of real prices that are representative of the risk factor.
 The bank must identify for the risk factor at least 24 real price (daily) observations per year over the
period used to calibrate the current ES model
 There must be no 90-day period in which fewer than four real price observations are identified in the
last 12 months
 The bank must identify for the risk factor at least 100 real (daily) price observations over the previous
12 months

Internal Models Approach – Stressed
Capital Add-On (SES)
Stressed Capital Add-On (SES)
This charge is for non-modellable risk factors (NMRF) 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
 In the event that a bank cannot provide a stress scenario which is acceptable for the supervisor, the bank will
have to use the maximum possible loss as the stress scenario.
 The aggregate capital charge for NMRF is calculated as
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;
- ISESNM, j is the stress scenario capital requirement for idiosyncratic equity non-modellable risk j
from the J risk factors aggregated with zero correlation
- SESNM, k is the stress scenario capital requirement for non-modellable risk k from K risk factors
- Rho (𝜌) is equal to 0.6

Sensitivities Charge – GIRR Delta Risk
Weights & Correlations
Buckets: bucketed by Curve Currency
Risk Weights
 Risk Weights are based on Tenor as shown in table
 For Inflation and Cross Currency basis risk factors, Risk Weight is 1.6%
 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 tenor that relates to WS 𝑘 (respectively WSl) and 𝜃 set at 3%.
 Between two sensitivities WS 𝑘 and WSl within the same bucket, different tenor 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 tenor 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 tenor 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)

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 18 are set out in the following table. Risk weights are the same for all tenors (ie 0.5
year, 1 year, 3 year, 5 year, 10 year) within each bucket

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
 All the three correlation parameters are equal to 1 where two names of sensitivities k and l are identical. If the names are not
identical, the following values should be used
 𝜌 𝑘l
(name) is 35% for buckets 1-16 and 80% for buckets 17 and 18
 𝜌 𝑘l
(tenor) is 65% for all buckets (1-18)
 𝜌 𝑘l
(basis) is 99.90% for all buckets (1-18)
 The above correlation calculation is also not applicable to "other sector" bucket (16). 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 aggregation of curvature CSR non-securitisation risk positions within the other sector bucket would be calculated
by the formula below.
 The correlation parameter γbc is set as follows
 γbc
(rating) is ) is equal to 50% where the two buckets b and c are both in
buckets 1 to 15 and have a different rating category (either IG or HY/NR).
γbc
(rating) is equal to 1 otherwise
 γbc
(sector) is equal to 1 if the two buckets have the same sector,
and to the numbers in the table otherwise:

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 tenors (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

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%.

Securitisations (non-CTP) Risk Weights &
Correlations
Correlations
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 tenors 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 aggregation of curvature CSR risk positions within the other sector bucket (ie bucket 16) would be calculated by the
formula below.
 The correlation between different buckets 1-24 (γbc) is set as 0%
 For aggregating delta CSR securitisations (non-CTP) risk positions between the other sector bucket (ie bucket 25) and buckets 1
to 24, the correlation parameter γbc is set at 1
 Bucket level capital requirements will be simply summed up to the overall risk class level capital requirements, with no
diversification or hedging effects recognised with any bucket.

Sensitivities Charge – Equity Delta Risk
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

Sensitivities Charge – Equity Delta Risk
Correlations
 The 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 rat or when both are related to the same Equity issuer name
 The correlation parameter 𝜌 𝑘l is as state below, where both sensitivities are to equity spot price
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).
5. 80% between two sensitivities within the same bucket that fall under either index bucket (bucket number 12 or 13)
 The same correlation parameter 𝜌 𝑘l as set out in above (1-4) apply, where both sensitivities are to equity repo rates.
 The correlation parameter 𝜌 𝑘l is set as each parameter specified in (1-4) multiplied by 99.9%, where each sensitivity is related to a different equity issuer
name
 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 aggregation of curvature equity risk positions within the other sector bucket (ie bucket 11) would be calculated by the formula:
 For aggregating delta equity risk positions across buckets 1 to 13, the correlation parameter γbc is set at:
 15% if bucket b and bucket c fall within bucket numbers 1 to 10
 0% if either of bucket b and bucket c is bucket 11
 75% if bucket b and bucket c are bucket numbers 12 and 13 (i.e. one is bucket 12, one is bucket 13)
 45% otherwise.

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

Sensitivities Charge – Commodity Delta
Risk Weights & Correlations
Correlations
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 tenors 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.

Sensitivities Charge – FX Delta Risk Weights
& Correlations
Buckets : Currency in which an instrument is denominated and the reporting currency (Currency pair)
Risk Weights
 A unique relative risk weight equal to 15% 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) and for currency pairs forming first-order crosses across these specified currency pairs, by
the Basel Committee, the above risk weight may at the discretion of the bank be divided by the square root of 2.
For example, EUR/AUD is not among the selected currency pairs specified by the Basel Committee, but is a first-
order cross of USD/EUR and USD/AUD
Correlations
 A uniform correlation parameter γbc equal to 60% is applied to all Currency pair buckets

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. The calculated risk weights are
shown in the table
Where
 𝑅W 𝜎 is set at 55%;
 𝐿Hrisk class is the liquidity horizon for a given risk class shown in the table below

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) = and 𝜌 𝑘l
(underlying maturity) =
 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;
 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 non 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 same as defined for GIRR above
Correlations between buckets
 For all risk classes, including GIRR, use same correlations as those used for Delta sensitivities

Sensitivities Charge – Curvature Risk
Buckets : Curvature buckets are same as corresponding Delta buckets for a given Risk Class
Risk Weights
 For FX and EQ risk classes, the curvature risk weigh is a relative shift equal to the respective delta risk weight.
 For GIRR, CSR and Commodity risk classes, the curvature risk weight is the parallel shift of all the tenors 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 0.25-year tenor (ie the most punitive tenor risk weight) is applied to all the tenors simultaneously
Correlations
 For aggregating curvature risk positions within a bucket, the curvature risk correlations 𝜌 𝑘l are determined by squaring
the corresponding delta correlation parameters 𝜌 𝑘l except for CSR non-securitisations and CSR securitisations (CTP).
 For CSR non-securitisations and CSR securitisations (CTP), the correlation parameter 𝜌 𝑘l = 𝜌 𝑘l
(name)2 , i.e., 𝜌 𝑘l
(tenor)1
and 𝜌 𝑘l
(basis) parameters are ignored (=1). This correlation parameter (𝜌 𝑘l
(name)) should be squared.
 For aggregating curvature risk positions across buckets, the curvature risk correlations γbc are determined by squaring
the corresponding delta correlation parameters γbc

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

FRTB Overview of Key Rules Changes

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