Final Document
SIMM Version 2.2

ISDA SIMMTM,1 Methodology, version 2.2 (based on v2.1.16: 25 July 2019)
Effective Date: December 1, 2019
Contextual Considerations
This document includes descriptions of initial margin calculations capturing Delta risk, Vega risk, Curvature risk,
Inter-curve basis risk and Concentration risk.

A.

General provisions

1.
This document describes the calculations and methodology for calculating the initial margin under the
ISDA Standard Initial Margin Model (SIMM) for non-cleared OTC derivatives.
2.
SIMM uses sensitivities as inputs. Risk factors and sensitivities must meet the definitions provided within
Section C.
3.
Sensitivities are used as inputs into aggregation formulae which are intended to recognize hedging anddiversification benefits of positions in different risk factors within an asset class. Risk weights and correlations areprovided in Sections D-I.
4.

This model includes complex trades, which should be handled in the same way as other trades.

B.

Structure of the methodology

5.

There are six risk classes:•

Interest Rate•

Credit (Qualifying)•

Credit (Non-Qualifying)•

Equity•Commodity•

FX

and the margin for each risk class is defined to be the sum of the Delta Margin, the Vega Margin, the Curvature
Margin and the Base Corr Margin (if applicable) for that risk class. That is
𝐼𝐼𝑀𝑀𝑋𝑋 = 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑛𝑛𝑋𝑋 + 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑛𝑛𝑋𝑋 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝑋𝑋 + 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝑛𝑛𝑋𝑋 ,for each risk class X, where the BaseCorrMargin term is only present in the Credit (Qualifying) risk class.
6.

There are four product classes:

1 Patent pending. This document is published by the International Swaps and Derivatives Association, Inc. (ISDA) and isprotected by copyright and other proprietary intellectual property rights. It cannot be used, revised or distributed except
solely for the purpose of a market participant’s own commercial transactions or as otherwise provided for by ISDA in a
written licensing agreement. If you are a service provider wishing to license ISDA SIMMTM or other ISDA intellectual
property, please contact isdalegal@isda.org. This notice may not be removed.

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Final Document
SIMM Version 2.2• Interest Rates and Foreign Exchange (RatesFX)• Credit• Equity• Commodity
Every trade is assigned to an individual product class and SIMM is considered separately for each product class.
Buckets are still defined in risk terms, but within each product class the risk class takes its component risks only
from trades of that product class. For example, equity derivatives would have risk in the Interest Rate risk class, aswell as the Equity risk class. But all those risks are kept separate from the risks of trades in the RatesFX productclass.
Within each product class, the initial margin (IM) for each of the six risk classes is calculated as inparagraph 5 above. The total margin for that product class is given by the formula:

𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = �� 𝐼𝐼𝑀𝑀𝑟𝑟2 + � � 𝜓𝜓𝑟𝑟𝑟𝑟 𝐼𝐼𝑀𝑀𝑟𝑟 𝐼𝐼𝑀𝑀𝑠𝑠 ,
𝑟𝑟

𝑟𝑟

𝑠𝑠≠𝑟𝑟

where product is one of the four product classes, and the sums on r and s are taken over the six risk classes. The
correlation matrix 𝜓𝜓𝑟𝑟𝑟𝑟 of correlations between the risk classes is given in Section K.
The total SIMM is the sum of these four product class SIMM values:
𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

The SIMM equation can be extended to incorporate notional-based add-ons for specified products and/or
multipliers to the individual product class SIMM values. Annex A contains the modified version of the SIMM inthat case.
7.
(Interest Rate risk only) The following step by step approach to capture delta risk should be applied tothe interest-rate risk class only:(a)Find a net sensitivity across instruments to each risk factor (k,i), where k is the rate tenor and i is theindex name of the sub yield curve, as defined in Sections C.1 and C.2 for the interest-rate risk class.

(b)

Weight the net sensitivity, s𝑘𝑘,𝑖𝑖 , to each risk factor (k,i) by the corresponding risk weight 𝑅𝑅𝑊𝑊𝑘𝑘 according
to the vertex structure set out in Section D.
𝑊𝑊𝑆𝑆𝑘𝑘,𝑖𝑖 = 𝑅𝑅𝑊𝑊𝑘𝑘 s𝑘𝑘,𝑖𝑖 𝐶𝐶𝑅𝑅𝑏𝑏 ,where CR is the concentration risk factor defined as:1

�∑𝑘𝑘,𝑖𝑖 𝑠𝑠𝑘𝑘,𝑖𝑖 � 2� �,
𝐶𝐶𝑅𝑅𝑏𝑏 = max �1, �
𝑇𝑇𝑏𝑏

for concentration threshold Tb, defined for each currency b in section J. Note that inflation sensitivities
to currency 𝑏𝑏 are included in �∑𝑘𝑘,𝑖𝑖 𝑠𝑠𝑘𝑘,𝑖𝑖 �, but cross-currency basis swap sensitivities are not. Neither shouldcross-currency basis swap sensitivities be scaled by the concentration risk factor.
(c)

The weighted sensitivities should then be aggregated within each currency. The sub-curve correlations
𝜙𝜙𝑖𝑖,𝑗𝑗 and the tenor correlation parameters 𝜌𝜌𝑘𝑘,𝑙𝑙 are set out in Section D.
2+�
𝐾𝐾 = �� 𝑊𝑊𝑆𝑆𝑘𝑘,𝑖𝑖
𝑖𝑖,𝑘𝑘

�

𝑖𝑖,𝑘𝑘 (𝑗𝑗,𝑙𝑙)≠(𝑖𝑖,𝑘𝑘)

𝜙𝜙𝑖𝑖,𝑗𝑗 𝜌𝜌𝑘𝑘,𝑙𝑙 𝑊𝑊𝑆𝑆𝑘𝑘,𝑖𝑖 𝑊𝑊𝑆𝑆𝑙𝑙,𝑗𝑗 .

Copyright © 2019 by International Swaps and Derivatives Association, Inc.

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Final Document
SIMM Version 2.2(d)Delta Margin amounts should then be aggregated across currencies within the risk class. The correlation
parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applicable are set out in Section D.
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = �� 𝐾𝐾𝑏𝑏2 + � � 𝛾𝛾𝑏𝑏𝑏𝑏 𝑔𝑔𝑏𝑏𝑏𝑏 𝑆𝑆𝑏𝑏 𝑆𝑆𝑐𝑐 ,𝑏𝑏 𝑐𝑐≠𝑏𝑏

𝑏𝑏

where

𝑆𝑆𝑏𝑏 = max �min �� 𝑊𝑊𝑆𝑆𝑘𝑘,𝑖𝑖 , 𝐾𝐾𝑏𝑏 � , −𝐾𝐾𝑏𝑏 � and 𝑔𝑔𝑏𝑏𝑏𝑏 =for all currencies b and c.

𝑖𝑖,𝑘𝑘min(𝐶𝐶𝑅𝑅𝑏𝑏 , 𝐶𝐶𝑅𝑅𝑐𝑐 ),max(𝐶𝐶𝑅𝑅𝑏𝑏 , 𝐶𝐶𝑅𝑅𝑐𝑐 )(non-Interest Rate risk classes) The following step by step approach to capture delta risk should be8.

separately applied to each risk class other than Interest Rate:(a)

Find a net sensitivity across instruments to each risk factor k, which are defined in Sections C.1 and C.2
for each risk class.

(b)

Weight the net sensitivity, s𝑘𝑘 , to each risk factor k by the corresponding risk weight 𝑅𝑅𝑊𝑊𝑘𝑘 according to thebucketing structure for each risk class set out in Sections E-I.
𝑊𝑊𝑆𝑆𝑘𝑘 = 𝑅𝑅𝑊𝑊𝑘𝑘 s𝑘𝑘 𝐶𝐶𝑅𝑅𝑘𝑘 ,where CRk is the concentration risk factor:
1�∑𝑗𝑗 𝑠𝑠𝑗𝑗 � 2
𝐶𝐶𝑅𝑅𝑘𝑘 = max �1, �� � for credit spread risk,
𝑇𝑇𝑏𝑏with the sum j taken over all the risk factors that have the same issuer and seniority as the risk factor k,
irrespective of the tenor or payment currency, and1|𝑠𝑠𝑘𝑘 | 2
𝐶𝐶𝑅𝑅𝑘𝑘 = max �1, �� � for equity, commodity, FX risk,
𝑇𝑇𝑏𝑏

where Tb is the concentration threshold for the bucket (or FX category) b, as given in Section J. Note thatbase correlation sensitivities are not included in the concentration risk, and the concentration risk factor
for those risk factors should be taken as 1.
(c)

Weighted sensitivities should then be aggregated within each bucket. The buckets and correlation
parameters applicable to each risk class are set out in Sections E-I.

where

(d)

𝐾𝐾 = �� 𝑊𝑊𝑆𝑆𝑘𝑘2 + � � 𝜌𝜌𝑘𝑘𝑘𝑘 𝑓𝑓𝑘𝑘𝑘𝑘 𝑊𝑊𝑆𝑆𝑘𝑘 𝑊𝑊𝑆𝑆𝑙𝑙 ,𝑘𝑘𝑘𝑘

𝑓𝑓𝑘𝑘𝑘𝑘 =𝑙𝑙≠𝑘𝑘min(𝐶𝐶𝑅𝑅𝑘𝑘 , 𝐶𝐶𝑅𝑅𝑙𝑙 ).
max(𝐶𝐶𝑅𝑅𝑘𝑘 , 𝐶𝐶𝑅𝑅𝑙𝑙 )Delta Margin amounts should then be aggregated across buckets within each risk class. The correlation
parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applicable to each risk class are set out in Sections E-I.
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = �� 𝐾𝐾𝑏𝑏2 + � � 𝛾𝛾𝑏𝑏𝑏𝑏 𝑆𝑆𝑏𝑏 𝑆𝑆𝑐𝑐 + 𝐾𝐾𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ,𝑏𝑏

𝑏𝑏 𝑐𝑐≠𝑏𝑏

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SIMM Version 2.2
where
𝑆𝑆𝑏𝑏 = max �min ��

for all risk factors in bucket b.
9.

𝐾𝐾

𝑘𝑘=1

𝑊𝑊𝑆𝑆𝑘𝑘 , 𝐾𝐾𝑏𝑏 � , −𝐾𝐾𝑏𝑏 �

Instruments that are options or include an option, including a prepayment option or have volatility

sensitivity (instruments subject to optionality) are subject to additional margin requirements for vega risk andcurvature risk, as described in paragraphs 10 and 11. Instruments not subject to optionality and with no volatility
sensitivity are not subject to vega risk or curvature risk.
10.

The following step by step approach to capture vega risk exposure should be separately applied to eachrisk class:(a)

For Interest Rate and Credit instruments, the volatility 𝜎𝜎𝑘𝑘𝑘𝑘 for risk factor k and maturity j, is defined tobe the implied at-the-money volatility of the swaption with expiry time equal to the tenor k, and at some
swap maturity j. The volatility can be quoted as normal volatility, log-normal volatility or similar.
In the case where k is the inflation risk-factor, the inflation volatility 𝜎𝜎𝑘𝑘𝑘𝑘 of an inflation swaption of typej is defined to be the at-the-money volatility of the swaption, where the type j comprises an initialinflation observation date and a final inflation observation date. The option expiry date shall be defined
to be the final inflation observation date, and risk should be expressed on a set of option expiries equal
to the same tenor buckets as interest-rate delta. The volatility can be quoted as normal volatility, lognormal volatility or similar.

(b)

For Equity, FX and Commodity instruments, the volatility 𝜎𝜎𝑘𝑘𝑘𝑘 of the risk factor k at each vol-tenor j isgiven by the following formula:𝜎𝜎𝑘𝑘𝑘𝑘 =𝑅𝑅𝑊𝑊𝑘𝑘 �365⁄14,𝛼𝛼where 𝛼𝛼 = Φ−1 (99%),

where 𝛼𝛼 is the 99th percentile of the cumulative standard normal distribution and 𝑅𝑅𝑊𝑊𝑘𝑘 is thecorresponding delta risk weight of the risk factor k, and the “vol-tenor” j is the option expiry time, whichshould use the same tenor buckets as interest-rate delta risk: 2 weeks, 1 month, 3 months, 6 months, 1
year, 2 years, 3 years, 5 years, 10 years, 15 years, 20 years and 30 years. For commodity index volatilities,
the risk weight to use is that of the “Indexes” bucket. For FX vega (which depends on a pair of currencies),
the risk weight to use here is the entry from the FX delta risk weight table, given in section I, whose row
is the FX volatility group of the first currency and whose column is the FX volatility group of the second
currency.
(c)

The vega risk for each instrument i to risk factor k is estimated using the formula:

𝑉𝑉𝑅𝑅𝑖𝑖𝑖𝑖 = � 𝜎𝜎𝑘𝑘𝑘𝑘
𝑗𝑗

where:••

𝜕𝜕𝜕𝜕𝑖𝑖,𝜕𝜕𝜕𝜕

𝑉𝑉𝑅𝑅𝑖𝑖𝑖𝑖 = 𝐻𝐻𝐻𝐻𝑅𝑅𝑐𝑐 � 𝜎𝜎𝑘𝑘𝑘𝑘
𝑗𝑗

for interest rates and credit, or𝜕𝜕𝜕𝜕𝑖𝑖, for equity, commodity and FX,𝜕𝜕𝜕𝜕𝜎𝜎𝑘𝑘𝑘𝑘 is the volatility defined in clauses (a) and (b);𝜕𝜕𝑉𝑉𝑖𝑖 /𝜕𝜕𝜕𝜕 is the sensitivity of the price of the instrument i with respect to the implied at-themoney volatility (i.e. “vega”), as defined in section C.3, but must match the definition used in

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SIMM Version 2.2
clause (a).
• 𝐻𝐻𝐻𝐻𝑅𝑅𝑐𝑐 is the historical volatility ratio for the risk class concerned, c, set out in sections G-I,
which corrects for inaccuracy in the volatility estimate 𝜎𝜎𝑘𝑘𝑘𝑘 .
For example, the 5-year Interest Rate vega is the sum of all vol-weighted interest rate caplet andswaption vegas which expire in 5 years’ time; the USD/JPY FX vega is the sum of all vol-weighted
USD/JPY FX vegas. For inflation, the inflation vega is the sum of all vol-weighted inflation swaption
vegas in the particular currency.
(d)Find a net vega risk exposure VRk across instruments i to each risk factor k, which are defined in Sections
C.1 and C.2, as well as the vega concentration risk factor. For interest-rate vega risk, these are given by
the formulas
1|∑𝑖𝑖𝑖𝑖 𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖 | 2
𝑉𝑉𝑅𝑅𝑘𝑘 = 𝑉𝑉𝑉𝑉𝑉𝑉 �� 𝑉𝑉𝑅𝑅𝑖𝑖𝑖𝑖 � 𝑉𝑉𝑉𝑉𝑅𝑅𝑏𝑏 , where 𝑉𝑉𝑉𝑉𝑅𝑅𝑏𝑏 = max �1, �� �,
𝑉𝑉𝑉𝑉𝑏𝑏𝑖𝑖

where b is the bucket which contains the risk factor k. For credit spread vega risk, the corresponding
formulas are
1

�∑𝑖𝑖𝑖𝑖 𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖 � 2
𝑉𝑉𝑉𝑉𝑘𝑘 = 𝑉𝑉𝑉𝑉𝑉𝑉 �� 𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖 � 𝑉𝑉𝑉𝑉𝑉𝑉𝑘𝑘 , where 𝑉𝑉𝑉𝑉𝑉𝑉𝑘𝑘 = max �1, �� �,
𝑉𝑉𝑉𝑉𝑏𝑏𝑖𝑖

where the sum j is taken over tenors of the same issuer/seniority curve as the risk factor k, irrespectiveof the tenor or payment currency. For Equity, FX and Commodity vega risk, the corresponding formulasare1|∑𝑖𝑖 𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖 | 2
𝑉𝑉𝑅𝑅𝑘𝑘 = 𝑉𝑉𝑉𝑉𝑉𝑉 �� 𝑉𝑉𝑅𝑅𝑖𝑖𝑖𝑖 � 𝑉𝑉𝑉𝑉𝑅𝑅𝑘𝑘 , where 𝑉𝑉𝑉𝑉𝑅𝑅𝑘𝑘 = max �1, �� �.
𝑉𝑉𝑉𝑉𝑏𝑏𝑖𝑖

Here VRW is the vega risk weight for the risk class concerned, set out in Sections D-I, and VTb is the vega
concentration threshold for bucket (or FX category) b, as given in section J. Note that there is special
treatment for index volatilities in Credit Qualifying, Equity and Commodity risk classes.
(e)

The vega risk exposure should then be aggregated within each bucket. The buckets and correlation
parameters applicable to each risk class are set out in Sections D-I.
𝐾𝐾𝑏𝑏 = �� 𝑉𝑉𝑉𝑉𝑘𝑘2 + � � 𝜌𝜌𝑘𝑘𝑘𝑘 𝑓𝑓𝑘𝑘𝑘𝑘 𝑉𝑉𝑅𝑅𝑘𝑘 𝑉𝑉𝑅𝑅𝑙𝑙 ,
𝑘𝑘

𝑘𝑘

𝑙𝑙≠𝑘𝑘

where the inner correlation adjustment factors 𝑓𝑓𝑘𝑘𝑘𝑘 are defined to be identically 1 in the interest-rate risk

(f)class and for all other risk classes are defined to be:min(𝑉𝑉𝑉𝑉𝑅𝑅𝑘𝑘 , 𝑉𝑉𝑉𝑉𝑅𝑅𝑙𝑙 )𝑓𝑓𝑘𝑘𝑘𝑘 =.
max(𝑉𝑉𝑉𝑉𝑅𝑅𝑘𝑘 , 𝑉𝑉𝑉𝑉𝑅𝑅𝑙𝑙 )Vega Margin should then be aggregated across buckets within each risk class. The correlation
parameters applicable to each risk class are set out in Sections D-I.

where

𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = �� 𝐾𝐾𝑏𝑏2 + � � 𝛾𝛾𝑏𝑏𝑏𝑏 𝑔𝑔𝑏𝑏𝑏𝑏 𝑆𝑆𝑏𝑏 𝑆𝑆𝐶𝐶 + 𝐾𝐾𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ,𝑏𝑏

𝑏𝑏 𝑐𝑐≠𝑏𝑏

𝐾𝐾

𝑆𝑆𝑏𝑏 = max �min �� 𝑉𝑉𝑅𝑅𝑘𝑘 , 𝐾𝐾𝑏𝑏 � , −𝐾𝐾𝑏𝑏 �,
𝑘𝑘=1

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for all risk factors in bucket b. The outer correlation adjustment factors 𝑔𝑔𝑏𝑏𝑏𝑏 are identically 1 for all risk
classes other than interest-rates, and for interest rates they are defined to be:
𝑔𝑔𝑏𝑏𝑏𝑏 =for all pairs of buckets b, c.
11.

min(𝑉𝑉𝑉𝑉𝑅𝑅𝑏𝑏 , 𝑉𝑉𝑉𝑉𝑅𝑅𝑐𝑐 )max(𝑉𝑉𝑉𝑉𝑅𝑅𝑏𝑏 , 𝑉𝑉𝑉𝑉𝑅𝑅𝑐𝑐 )The following step by step approach to capture curvature risk exposure should be separately applied toeach risk class:(a)

The curvature risk exposure for each instrument i to risk factor k is estimated using the formula:
𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝑖𝑖 = � 𝑆𝑆𝑆𝑆�𝑡𝑡𝑘𝑘𝑘𝑘 �𝜎𝜎𝑘𝑘𝑘𝑘
𝑗𝑗

where:•••

ExpirySF

𝜕𝜕𝑉𝑉𝑖𝑖,𝜕𝜕𝜕𝜕

𝜎𝜎𝑘𝑘𝑘𝑘 and 𝜕𝜕𝑉𝑉𝑖𝑖 /𝜕𝜕𝜕𝜕 are the volatility and vega defined in paragraph 10(a-c) above.
𝑡𝑡𝑘𝑘𝑘𝑘 is the expiry time (in calendar days) from the valuation date until the expiry date of thestandard option corresponding to this volatility and vega.
𝑆𝑆𝑆𝑆(𝑡𝑡) is the value of the scaling function obtained from the linkage between vega and gamma
for vanilla options.
14 days
𝑆𝑆𝑆𝑆(𝑡𝑡) = 0.5 min �1,
�.
𝑡𝑡 days
The scaling function is a function of expiry only, which is independent of both vega and vol, as
shown in the example table below.

2w
50.0%

1m
23.0%

3m
7.7%

6m
3.8%

12m
1.9%

2y
1.0%

3y
0.6%

5y
0.4%

10y
0.2%

Here, we convert tenors to calendar days using the convention that “12m” equals 365 calendar
days, with pro-rata scaling for other tenors so that 1m = 365/12 days and 5y = 365*5 days.
(b) The curvature risk exposure 𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝑖𝑖 then can be netted across instrument i to each risk factor k, which aredefined in Sections C.1 and C.2. Note that the same special treatment as for vega applies for indexes in
Credit, Equity and Commodity risk classes. The curvature risk exposure for bucket 12 (Volatility Indexes)in the equity risk class shall be taken to be zero.
(c)

The curvature risk exposure should then be aggregated within each bucket using the following formula:

where
•
(d)

2
2
𝐾𝐾𝑏𝑏 = �� 𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘+ � � 𝜌𝜌𝑘𝑘𝑘𝑘
𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘 𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑙𝑙 ,
𝑘𝑘

𝑘𝑘

𝑙𝑙≠𝑘𝑘

𝜌𝜌𝑘𝑘𝑘𝑘 is the assumed correlation applicable to each risk class as set out in Sections D-I. Note the2rather than 𝜌𝜌𝑘𝑘𝑘𝑘 .
use of 𝜌𝜌𝑘𝑘𝑘𝑘

Margin should then be aggregated across buckets within each risk class:𝜃𝜃 = min �∑𝑏𝑏,𝑘𝑘 𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘∑𝑏𝑏,𝑘𝑘�𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘 �, 0� ,and 𝜆𝜆 = (Φ−1 (99.5%)2 − 1)(1 + 𝜃𝜃) − 𝜃𝜃,

where the sums are taken over all the non-residual buckets in the risk class, and Φ−1 (99.5%) is the 99.5th

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percentile of the standard normal distribution. Then the non-residual curvature margin is

where

2
𝑆𝑆𝑏𝑏 𝑆𝑆𝑐𝑐 , 0�,
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛−𝑟𝑟𝑟𝑟𝑟𝑟 = max �� 𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘 + 𝜆𝜆�� 𝐾𝐾𝑏𝑏2 + � � 𝛾𝛾𝑏𝑏𝑏𝑏
𝑏𝑏,𝑘𝑘𝑏𝑏 𝑐𝑐≠𝑏𝑏

𝑏𝑏

𝑆𝑆𝑏𝑏 = max �min �� 𝐶𝐶𝐶𝐶𝑅𝑅𝑏𝑏,𝑘𝑘 , 𝐾𝐾𝑏𝑏 � , −𝐾𝐾𝑏𝑏 � .

Similarly, the residual equivalents are defined as𝑘𝑘∑𝑘𝑘 𝐶𝐶𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘, 0� ,
𝜃𝜃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = min �∑𝑘𝑘�𝐶𝐶𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘 �

and

𝜆𝜆𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = �Φ−1 (99.5%)2 − 1�(1 + 𝜃𝜃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ) − 𝜃𝜃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ,Here•

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = max �� 𝐶𝐶𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟,𝑘𝑘 + 𝜆𝜆𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝐾𝐾𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 , 0�𝑘𝑘

the correlation parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applicable to each risk class are set out in Sections D-I. Note the2rather than 𝛾𝛾𝑏𝑏𝑏𝑏 .
use of 𝛾𝛾𝑏𝑏𝑏𝑏

Then the total curvature margin is defined to be the sum of the two terms:

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛−𝑟𝑟𝑟𝑟𝑟𝑟 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑛𝑛𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 .

−2
For the interest-rate risk class only, the CurvatureMargin must be multiplied by a scale factor of 𝐻𝐻𝐻𝐻𝑅𝑅𝐼𝐼𝐼𝐼,
where 𝐻𝐻𝐻𝐻𝑅𝑅𝐼𝐼𝐼𝐼 is the historical volatility ratio for the interest-rate risk class.

12.
Credit Qualifying Only: Instruments whose price is sensitive to correlation between the defaults ofdifferent credits within an index or basket, such as CDO tranches, are subject to Base Correlation margin charge
described in paragraph 13. Instruments not sensitive to base correlation are not subject to base correlation margin
requirements.
13.
The following step by step approach to capture Base Correlation risk exposure should be applied to theCredit (Qualifying) risk class:(a)Find a net sensitivity across instruments to each Base Correlation risk factor k, where k is the index familysuch as CDX IG.
(b)
Weight the net sensitivity, 𝑠𝑠𝑘𝑘 , to each risk factor k by the corresponding risk weight 𝑅𝑅𝑊𝑊𝑘𝑘 , specified in
section E:
𝑊𝑊𝑆𝑆𝑘𝑘 = 𝑅𝑅𝑊𝑊𝑘𝑘 𝑠𝑠𝑘𝑘 .

(c)Weighted sensitivities should then be aggregated to give the Base Correlation Margin, as follows:

𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = �� 𝑊𝑊𝑆𝑆𝑘𝑘2 + � � 𝜌𝜌𝑘𝑘𝑘𝑘 𝑊𝑊𝑆𝑆𝑘𝑘 𝑊𝑊𝑆𝑆𝑙𝑙 .
𝑘𝑘

𝑘𝑘

𝑙𝑙≠𝑘𝑘

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The correlation parameters are set out in Section E.

C.

Definition of the risk factors and the sensitivities

C.1

Definition of the risk factors

14.

The Interest Rate risk factors are the 12 yields at the following vertices, for each currency: two weeks, 1month, 3 months, 6 months, 1 year, 2 years, 3 years, 5 years, 10 years, 15 years, 20 years and 30 years.
The relevant yield curve is the yield curve of the currency in which an instrument is denominated.
For a given currency, there are a number of sub yield curves used, named “OIS”, “Libor1m”, “Libor3m”,“Libor6m”, “Libor12m” and (for USD only) “Prime” and “Municipal”. Each sub curve has an index name i. Risk
should be separately bucketed by currency, tenor and curve index, expressed as risk to the outright rate of the sub
curve. Any sub curve not given on the above list should be mapped to its closest equivalent.
The Interest Rate risk factors also include a flat inflation rate for each currency. When at least one
contractual payment obligation depends on an inflation rate, the inflation rate for the relevant currency is used asa risk factor. All sensitivities to inflation rates for the same currency are fully offset.
For cross-currency swap products whose notional exchange is eligible for exclusion from the margin
calculation, the interest rate risk factors also include a flat cross-currency basis swap spread for each currency.
Cross-currency basis swap spreads should be quoted as a spread to the non-USD Libor versus a flat USD Libor leg.
All sensitivities to cross-currency basis swap spreads for the same currency are fully offset.
If fallback provisions take effect for a Libor or IBOR rate to an RFR-based fallback, then the relevant Liborsub curve should no longer be used for risk to that index and the OIS sub curve should be used instead. If fallback
provisions take effect for a Libor or IBOR rate which is used in a standard cross-currency basis swap leg, then thatleg should be redefined to use the RFR which would be used to calculate the fallback rate in the 2006 ISDA
Definitions.
15.

The Credit Qualifying risk factors are five credit spreads for each issuer/seniority pair, separately by

payment currency, at each of the following vertices: 1 year, 2 years, 3 years, 5 years and 10 years.
For a given issuer/seniority, if there is more than one relevant credit spread curve, then the credit spreadrisk at each vertex should be the net sum of risk at that vertex over all the credit spread curves of that issuer andseniority, which may differ by documentation (such as restructuring clause), but not by currency. Note that delta
and vega sensitivities arising from different payment currencies (such as Quanto CDS) are considered different risk
factors to the same issuer/seniority from each other.
For Credit Qualifying indexes and bespoke baskets (including securitizations and non-securitizations),
delta sensitivities should be computed to the underlying issuer/seniority risk factors. Vega sensitivities of credit
indexes need not be allocated to underlying risk factors, but rather the entire index vega risk should be classed
into the appropriate Credit Qualifying bucket, using the Residual bucket for cross-sector indexes.
The Credit Qualifying risk factors can also include Base Correlation risks from CDO tranches on the CDX
or iTraxx families of credit indices. There is one flat risk factor for each index family. Base Correlation risks to thesame index family (such as CDX IG, iTraxx Main, and so on) should be fully offset, irrespective of series, maturity
or detachment point.
16.

The Credit Non-Qualifying risk factors are five credit spreads for each issuer/tranche at each of thefollowing vertices: 1 year, 2 years, 3 years, 5 years and 10 years.

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Sensitivities should be computed to the tranche. For a given tranche, if there is more than one relevant
credit spread curve, then the credit spread risk at each vertex should be the net sum of risk at that vertex over all
the credit spread curves of that tranche. Vega sensitivities of credit indexes need not be allocated to underlying
issuers, but rather the entire index vega should be classed into the appropriate Non-qualifying bucket, using theResidual bucket for cross-sector indexes.
17.

The Equity risk factors are all the equity prices: each equity spot price is a risk factor. Sensitivities toequity indices, funds and ETFs can be handled in one of two ways: either (standard preferred approach) the entire
delta and can be put into the “Indexes, Funds, ETFs” Equity bucket, or (alternative approach if bilaterally agreed)
the delta can be allocated back to individual equities. The choice between standard and alternative approachshould be made on a portfolio-level basis. Delta sensitivities to bespoke baskets should always be allocated backto individual equities. Vega sensitivities of equity indexes, funds and ETFs need not be allocated back to individual
equities, but rather the entire vega risk should be classed into the “Indexes, Funds, ETFs” Equity bucket. Vegasensitivities to bespoke baskets should be allocated back to individual equities. Note that not all institutions may
be able to perform the allocation of vega for equities as described, however, it is the preferred approach. For equity
volatility indexes, the index risk should be treated as equity volatility risk and put into the “Volatility Index“ bucket.
18.

The Commodity risk factors are all the commodity prices: each commodity spot price is a risk factor.

Examples include “Coal Europe”, “Precious Metals Gold” and “Livestock Lean Hogs”. Risks to commodity forward
prices should be allocated back to spot price risks and aggregated, assuming that each commodity forward curve
moves in parallel. Sensitivities to commodity indices can be handled in one of two ways: either (standard approach)the entire delta can be put into the “Indexes” bucket, or (advanced approach) the delta can be allocated back toindividual commodities. The choice between standard and advanced approaches should be made on a portfoliolevel basis. Delta sensitivities to bespoke baskets should always be allocated back to individual commodities. Vegasensitivities of commodity indexes should not be allocated back to individual commodities, but rather the entire
index vega risk should be classed into the “Indexes” bucket.
19.

The FX risk factors are all the exchange rates between the calculation currency and any currency, or

currency of any FX cross rate, on which the value of an instrument may depend. This excludes the calculation
currency itself. The FX vega and curvature risk factors are all the currency pairs to which an instrument has FX
volatility risk.

C.2

Definition of “sensitivity” for delta margin calculation

20.

The following sections define the sensitivity s that should be used as input into the delta margin

calculation. The forward difference is specified in each section for illustrative purposes:
For Interest Rate and Credit:
For Equity, Commodity, and FX risk:

𝑠𝑠 = 𝑉𝑉(𝑥𝑥 + 1bp) − 𝑉𝑉(𝑥𝑥)𝑠𝑠 = 𝑉𝑉(𝑥𝑥 + 1%. 𝑥𝑥) − 𝑉𝑉(𝑥𝑥)where:• s is the sensitivity to the risk factor x• V(x) is the value of the instrument, given the value of the risk factor x.

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21.

However, banks may also make use of the central or backward difference methods, or use a smaller shock

size and scale-up:
For Interest Rate and Credit:

𝑠𝑠 = 𝑉𝑉(𝑥𝑥 + 0.5bp) − 𝑉𝑉(𝑥𝑥 − 0.5bp)
𝑠𝑠 = 𝑉𝑉(𝑥𝑥) − 𝑉𝑉(𝑥𝑥 − 1bp)
𝑠𝑠 = (𝑉𝑉(𝑥𝑥 + 𝜀𝜀. 1bp) − 𝑉𝑉(𝑥𝑥))/𝜀𝜀, where 0 < |𝜀𝜀| ≤ 1.

For Equity, Commodity and FX risk:
𝑠𝑠 = 𝑉𝑉(𝑥𝑥 + 0.5%. 𝑥𝑥) − 𝑉𝑉(𝑥𝑥 − 0.5%. 𝑥𝑥)
𝑠𝑠 = 𝑉𝑉(𝑥𝑥) − 𝑉𝑉(𝑥𝑥 − 1%. 𝑥𝑥)
𝑠𝑠 = (𝑉𝑉(𝑥𝑥 + 1%. 𝜀𝜀. 𝑥𝑥) − 𝑉𝑉(𝑥𝑥))/𝜀𝜀, where 0 < |𝜀𝜀| ≤ 1.
For Interest Rate risk factors, the sensitivity is defined as the PV01.

22.

The PV01 of an instrument i with respect to tenor t of the risk-free curve r (ie the sensitivity of
instrument i with respect to the risk factor 𝑟𝑟𝑡𝑡 ) is defined as:with𝑠𝑠(𝑖𝑖, 𝑟𝑟𝑡𝑡 ) = 𝑉𝑉𝑖𝑖 (𝑟𝑟𝑡𝑡 + 1bp, 𝑐𝑐𝑠𝑠𝑡𝑡 ) − 𝑉𝑉𝑖𝑖 (𝑟𝑟𝑡𝑡 , 𝑐𝑐𝑠𝑠𝑡𝑡 )𝑟𝑟𝑡𝑡 : the risk-free interest rate at tenor t
𝑐𝑐𝑠𝑠𝑡𝑡 : the credit spread at tenor t
𝑉𝑉𝑖𝑖 : the market value of an instrument i as a function of the risk-free interest rate and credit
spread curve• 1bp: 1 basis point, ie 0.0001 or 0.01%.
For the interest rate risk factors, “market rates” (and not “zero coupon rates”) should be used toconstruct the risk-free yield curve.
•••

For Credit non-securitisation risk factors, the sensitivity is defined as the CS01.

23.

The CS01 of an instrument with respect to tenor t is defined as:𝑠𝑠(𝑖𝑖, 𝑐𝑐𝑠𝑠𝑡𝑡 ) = 𝑉𝑉𝑖𝑖 (𝑟𝑟𝑡𝑡 , 𝑐𝑐𝑠𝑠𝑡𝑡 + 1bp) − 𝑉𝑉𝑖𝑖 (𝑟𝑟𝑡𝑡 , 𝑐𝑐𝑠𝑠𝑡𝑡 )For Credit Qualifying and Non-Qualifying securitisations, including nth-to-default risk factors, the24.

sensitivity is defined as the CS01.
If all the following criteria are met, the position is deemed to be a qualifying securitisation, and the CS01 (as definedfor Credit (non-securitisations) above) should be computed with respect to the names underlying the securitisation
or nth-to-default instrument:•

The positions are not re-securitisation positions, nor derivatives of securitisation exposures that do notprovide a pro-rata share in the proceeds of a securitisation tranche•••

All reference entities are single-name products, including single-name credit derivatives, for which aliquid two-way market exists (see below), including traded indices on these reference entities.
The instrument does not reference an underlying that would be treated as a retail exposure, a residential
mortgage exposure, or a commercial mortgage exposure under the standardised approach to credit risk.
The instrument does not reference a claim on a special purpose entity

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If any of these criteria are not met, the position is deemed to be non-qualifying, and then the CS01 should be
calculated with respect to the spread of the instrument rather than the spread of the underlying of the
instruments.
A two-way market is deemed to exist where there are independent bona fide offers to buy and sell so that a pricereasonably related to the last sales price or current bona fide competitive bid and offer quotations can be
determined within one day and settled at such price within a relatively short time conforming to trade custom.
25.

For Credit Qualifying Base Correlation risk factors, the sensitivity is defined as the BC01.
The BC01 is the change in value for a 1 percentage point increase in the Base Correlation level, that is thesensitivity 𝑠𝑠𝑖𝑖𝑖𝑖 defined as
where

26.

𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑉𝑉𝑖𝑖 (𝐵𝐵𝐶𝐶𝑘𝑘 + 1%) − 𝑉𝑉𝑖𝑖 (𝐵𝐵𝐶𝐶𝑘𝑘 )•k is a given credit index family such as CDX IG or iTraxx Main•

𝐵𝐵𝐶𝐶𝑘𝑘 is the Base Correlation curve/surface for index k, with numerical values such as 0.55.

•

1% is one percentage point of correlation, that is 0.01.

•

𝑉𝑉𝑖𝑖 (𝐵𝐵𝐶𝐶𝑘𝑘 ) is the value of instrument i as a function of the Base Correlation for index k.

For Equity risk factors, the sensitivity is defined as follows:
The value change of an instrument with respect to a 1 percentage point relative change of the equity

price:
with

27.

•
•
•

𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑉𝑉𝑖𝑖 (𝐸𝐸𝑄𝑄𝑘𝑘 + 1%. 𝐸𝐸𝑄𝑄𝑘𝑘 ) − 𝑉𝑉𝑖𝑖 (𝐸𝐸𝑄𝑄𝑘𝑘 )k : a given equity
𝐸𝐸𝑄𝑄𝑘𝑘 : the market value of equity k𝑉𝑉𝑖𝑖 : the market value of instrument i as a function of the price of equity k

For Commodity risk factors, the sensitivity is defined as follows:

The value change of an instrument with respect to a 1 percentage point relative change of thecommodity price:
with

28.

•
•
•

𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑉𝑉𝑖𝑖 (𝐶𝐶𝐶𝐶𝑌𝑌𝑘𝑘 + 1%. 𝐶𝐶𝐶𝐶𝑌𝑌𝑘𝑘 ) − 𝑉𝑉𝑖𝑖 (𝐶𝐶𝐶𝐶𝑌𝑌𝑘𝑘 )k: a given commodity
𝐶𝐶𝐶𝐶𝑌𝑌𝑘𝑘 : the market value of commodity k𝑉𝑉𝑖𝑖 : the market value of instrument i as a function of the price of commodity k

For FX risk factors, the sensitivity is defined as follows:

The value change of an instrument with respect to a 1 percentage point relative change of the
FX rate:
with

•
•
•

𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑉𝑉𝑖𝑖 (𝐹𝐹𝑋𝑋𝑘𝑘 + 1%. 𝐹𝐹𝑋𝑋𝑘𝑘 ) − 𝑉𝑉𝑖𝑖 (𝐹𝐹𝑋𝑋𝑘𝑘 ),k: a given currency, other than the calculation currency
𝐹𝐹𝐹𝐹𝑘𝑘 : the spot exchange rate between currency k and the calculation currency, expressed inunits of the calculation currency for one unit of currency k.
𝑉𝑉𝑖𝑖 : the market value of instrument i as a function of the exchange rate k

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The FX sensitivity of the calculation currency itself should be excluded from the calculation.
29.

When computing a first order sensitivity for instruments subject to optionality, it is recommended thatthe volatility under the bump is adjusted per prevailing market practice in each risk class.

C.3

Definition of “sensitivity” for vega and curvature margin calculation

30.

The following paragraphs define the sensitivity 𝜕𝜕𝑉𝑉𝑖𝑖 /𝜕𝜕𝜕𝜕 that should be used as input into the vega andcurvature margin calculations in paragraphs 10 and 11. The vega sensitivity to the implied volatility risk factor 𝜎𝜎 isdefined as:

𝜕𝜕𝑉𝑉𝑖𝑖= 𝑉𝑉(𝜎𝜎 + 1) − 𝑉𝑉( 𝜎𝜎),𝜕𝜕𝜕𝜕

where:• 𝑉𝑉(𝜎𝜎) is the value of the instrument given the implied volatility 𝜎𝜎 of the risk factor, whilst
keeping other inputs, including skew and smile, constant,• the implied volatility 𝜎𝜎 should be the log-normal volatility, except in the case of Interest Rate
and Credit risks when it can be the normal volatility or log-normal volatility, or similar, butmust match the definition used in paragraph 10 clause (a)• for Equity, FX and Commodity instruments, the units of 𝜎𝜎 must be percentages of log-normal
volatility, so that 20% is represented as 20. A shock to 𝜎𝜎 of 1 unit therefore represents anincrease in volatility of 1%.
• for Interest Rate and Credit instruments, the units of 𝜎𝜎 must match the units of the volatility
𝜎𝜎𝑘𝑘𝑘𝑘 used in paragraph 10 clause (a).
31.

The central or backward difference methods may also be used, or use a smaller shock size and scale-up:
𝜕𝜕𝑉𝑉𝑖𝑖= 𝑉𝑉(𝜎𝜎 + 0.5) − 𝑉𝑉(𝜎𝜎 − 0.5), or𝜕𝜕𝜕𝜕𝜕𝜕𝑉𝑉𝑖𝑖= 𝑉𝑉(𝜎𝜎) − 𝑉𝑉(𝜎𝜎 − 1), or𝜕𝜕𝜕𝜕𝜕𝜕𝑉𝑉𝑖𝑖 𝑉𝑉(𝜎𝜎 + 𝜖𝜖) − 𝑉𝑉(𝜎𝜎)=, where 0 < |𝜖𝜖| ≤ 1.
𝜕𝜕𝜎𝜎𝜖𝜖

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D.

Interest Rate risk

D.1

Interest Rate – Risk weights

32.

The set of risk-free yield curves within each currency is considered to be a separate bucket.

33.

The risk weights 𝑅𝑅𝑊𝑊𝑘𝑘 are set out in the following tables:(1) There is one table for regular volatility currencies, which are defined to be: the US Dollar (USD), Euro
(EUR), British Pound (GBP), Swiss Franc (CHF), Australian Dollar (AUD), New Zealand Dollar (NZD), Canadian Dollar(CAD), Swedish Krona (SEK), Norwegian Krone (NOK), Danish Krona (DKK), Hong Kong Dollar (HKD), South Korean
Won (KRW), Singapore Dollar (SGD), and Taiwanese Dollar (TWD).
(2) There is a second table for low-volatility currencies, which are defined to be the Japanese Yen (JPY)
only.
(3) There is a third table for high-volatility currencies, which are defined to be all other currencies.
Table 1: Risk weights per vertex (regular currencies)
2w

1m

116

106

3m
94

6m
71

1yr
59

2yr
52

3yr
49

5yr
51

10yr
51

15yr
51

20yr
54

30yr
62

3yr
22

5yr
20

10yr
20

15yr
20

20yr
22

30yr
27

3yr
104

5yr
102

10yr
103

15yr
99

20yr
99

30yr
100

Table 2: Risk weights per vertex (low-volatility currencies)
2w

1m

14

20

3m
10

6m
10

1yr
14

2yr
20

Table 3: Risk weights per vertex (high-volatility currencies)
2w

1m

85

80

3m
79

6m
86

1yr
97

2yr
102

The risk weight for any currency’s inflation rate is 47.
The risk weight for any currency's cross-currency basis swap spread is 20.
34.

The historical volatility ratio, HVR, for the interest-rate risk class is 0.53.

35.

The vega risk weight, VRW, for the Interest Rate risk class is 0.16.

D.2

Interest Rate – Correlations

36.

The correlation matrix below for risk exposures should be used

Correlations for aggregated weighted sensitivities or risk exposures

2w
2w

1m

3m

6m

1yr

2yr

3yr

5yr

10yr

15yr

20yr

30yr

69%

64%

55%

34%

21%

16%

11%

6%

1%

0%

-2%

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2w

1m

3m

6m

1yr

2yr

3yr

5yr

10yr

15yr

20yr

30yr

79%

65%

50%

39%

33%

26%

20%

14%

11%

9%

85%

67%

53%

46%

37%

29%

22%

19%

16%

85%

72%

65%

56%

46%

38%

34%

30%

93%

88%

78%

66%

60%

56%

52%

91%

81%

75%

72%

68%

96%

87%

83%

80%

76%

95%

92%

89%

86%

98%

97%

95%

99%

98%

1m

69%

3m

64%

79%

6m

55%

65%

85%

1yr

34%

50%

67%

85%

2yr

21%

39%

53%

72%

93%

3yr

16%

33%

46%

65%

88%

98%

5yr

11%

26%

37%

56%

78%

91%

96%

10yr

6%

20%

29%

46%

66%

81%

87%

95%

15yr

1%

14%

22%

38%

60%

75%

83%

92%

98%

20yr

0%

11%

19%

34%

56%

72%

80%

89%

97%

99%

30yr

-2%

9%

16%

30%

52%

68%

76%

86%

95%

98%

98%

99%
99%

For sub-curves, the correlation 𝜙𝜙𝑖𝑖,𝑗𝑗 between any two sub-curves of the same currency is (to one decimal

place) 98.5%

For aggregated weighted sensitivities or risk exposures, the correlation between the inflation rate andany yield for the same currency (and the correlation between the inflation volatility and any interest-rate volatility
for the same currency) is 39%
For aggregated weighted sensitivities or risk exposures, the correlation between the cross-currency basis
swap spread and any yield or inflation rate for the same currency is 13%
37. The parameter 𝛾𝛾𝑏𝑏𝑏𝑏 = 22% should be used for aggregating across different currencies.

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E.

Credit Qualifying risk

E.1

Credit Qualifying – Risk weights

38.

Sensitivities or risk exposures to an issuer/seniority should first be assigned to a bucket according to thefollowing table:
Bucket number
1

Credit quality

SectorSovereigns including central banks

2

Financials including government-backed financials

3

Investment grade Basic materials, energy, industrials
Consumer(IG)
Technology, telecommunications
Health care, utilities, local government, government-backed corporates(non- financial)
Sovereigns including central banks
Financials including government backed financials
Basic materials, energy, industrials
High yield (HY) &Consumer
non-rated (NR)Technology, telecommunications
Health care, utilities, local government, government-backed corporates(non- financial)

4
5
6
7
8
9
10
11
12
ResidualSensitivities must be distinguished depending on the payment currency of the trade (such as Quanto CDS andnon-Quanto CDS). No initial netting or aggregation is applied between position sensitivities from different
payment currencies (except as then described in paragraph 42).

39.

The same risk weight should be used for all vertices (1yr, 2yr, 3yr, 5yr, 10yr), according to bucket, as set

out in the following table:
Bucket
1
2
3
4
5
6
7
8
9
10
11
12
Residual

Risk weight
72
97
75
53
45
53
165
250
191
179
132
129
250

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40. The vega risk weight, VRW, for the Credit risk class is 0.39.
41. The Base Correlation risk weight is 7 for all index families.

E.2

Credit Qualifying – Correlations

42.

The correlation parameters 𝜌𝜌𝑘𝑘𝑘𝑘 applying to sensitivity or risk exposure pairs within the same bucket are

set out in the following table:

Same issuer/seniority,
different vertex or currency

Different issuer/seniority

Aggregate sensitivities

95%

41%

Residual bucket

50%

50%

Herein “currency” refers to the payment currency of the sensitivity if there are sensitivities to multiple
payment currencies (such as Quanto CDS and non-Quanto CDS), which will not be fully offset.

43.

The correlation parameter 𝜌𝜌𝑘𝑘𝑘𝑘 applying to Base Correlation risks across different index families is 14%.

The correlation parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applying to sensitivity or risk exposure pairs across different non-residual

buckets is set out in the following table:
Bucket
1
2
3
4
5
6
7
8
9
10
11
12

1
43%
42%
41%
43%
39%
40%
35%
37%
37%
37%
32%

2
43%
46%
46%
47%
44%
34%
39%
41%
41%
41%
35%

3
42%
46%
47%
48%
45%
34%
38%
42%
42%
41%
36%

4
41%
46%
47%
48%
45%
34%
37%
40%
42%
41%
35%

5
43%
47%
48%
48%
47%
34%
37%
40%
42%
43%
36%

6
39%
44%
45%
45%
47%
32%
35%
38%
39%
39%
34%

7
40%
34%
34%
34%
34%
32%
26%
31%
30%
29%
26%

8
35%
39%
38%
37%
37%
35%
26%
34%
33%
33%
30%

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9
37%
41%
42%
40%
40%
38%
31%
34%
37%
36%
33%

10
37%
41%
42%
42%
42%
39%
30%
33%
37%
38%
32%

11
37%
41%
41%
41%
43%
39%
29%
33%
36%
38%

12
32%
35%
36%
35%
36%
34%
26%
30%
33%
32%
32%

32%

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F.

Credit Non-Qualifying risk

44.

Sensitivities to credit spread risk arising from non-qualifying securitisation positions are treated according

to the risk weights and correlations specified in the following paragraphs.

F.1

Credit Non-Qualifying – Risk weights

45.

Sensitivities or risk exposures should first be assigned to a bucket according to the following table:

Bucket number
1

Credit quality
Investment grade (IG)Sector
RMBS/CMBS

2

High yield (HY) & non-rated (NR)

RMBS/CMBS

Residual
If it is not possible to allocate a sensitivity or risk exposure to one of these buckets (for example, because data on
categorical variables is not available), then the position must be allocated to the “Residual bucket”.
46.

The risk weights are set out in the following table:
Bucket number
1

Risk weight
100

2

1600

Residual

1600

47. The vega risk weight, VRW, for Credit Non-Qualifying is 0.39.

F.2

Credit Non-Qualifying – Correlations

48.

For the other buckets, the correlation parameters 𝜌𝜌𝑘𝑘𝑘𝑘 applying to sensitivity or risk exposure pairs within

the same bucket are set out in the following table:

49.

Same group name(such as CMBX, IOS, MBX, ABX)

Different group name

Aggregate sensitivities

43%

15%

Residual bucket

50%

50%

The correlation parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applying to sensitivity or risk exposure pairs across different buckets is

set out in the following table:

Correlation
Non-residual bucket to non-residual bucket

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G.

Equity risk

G.1

Equity – Risk weights

50.

Sensitivities or risk exposures should first be assigned to a bucket according to the buckets defined in thefollowing table:
Bucket number

Size

RegionEmerging markets

SectorConsumer goods and services, transportation andstorage, administrative and support service activities,
utilities
Telecommunications, industrials
Basic materials, energy, agriculture, manufacturing,mining and quarrying
Financials including gov’t-backed financials, realestate activities, technology
Consumer goods and services, transportation andstorage, administrative and support service activities,
utilities
Telecommunications, industrials
Basic materials, energy, agriculture, manufacturing,mining and quarrying
Financials including gov’t-backed financials, realestate activities, technology
All sectors

Developed markets
AllAll

All sectors
Indexes, Funds, ETFs
Volatility Indexes

1
2

Emerging markets

3
4

Large

5
6

Developed markets

7
8
9
10
11
12
51.

Small
All
All

“Large” is defined as a market capitalisation equal to or greater than USD 2 billion and “small” is defined

as a market capitalisation of less than USD 2 billion.
52.

“Market capitalisation” is defined as the sum of the market capitalisations of the same legal entity orgroup of legal entities across all stock markets globally.
53.

The developed markets are defined as: Canada, US, 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.
54.

The sectors definition is the one generally used in the market. When allocating an equity position to aparticular bucket, the bank must prove that the equity issuer’s most material activity indeed corresponds to thebucket’s definition. Acceptable proofs might be external providers’ information, or internal analysis.
55.

For multinational multi-sector equity issuers, the allocation to a particular bucket must be done according

to the most material region and sector the issuer operates in.
56.

If it is not possible to allocate a position to one of these buckets (for example, because data on categoricalvariables is not available) then the position must be allocated to a “Residual bucket”. Risk weights should be
assigned to each notional position as in the following table:

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Bucket
1
2
3
4
5
6
7
8
9
10
11
12
Residual

Risk Weight
22
26
29
26
19
21
25
24
30
29
17
17
30

57. The historical volatility ratio, HVR, for the equity risk class is 61%.
58. The vega risk weight, VRW, for the equity risk class is 0.26 for all buckets except bucket 12 for which thevega risk weight is 0.62.

G.2

Equity – Correlations

59.

The correlation parameters 𝜌𝜌𝑘𝑘𝑘𝑘 applying to sensitivity or risk exposure pairs within the same bucket are

set out in the following table:

60.

Bucket number
1

Correlation
16%

2

21%

3

28%

4

25%

5

20%

6

30%

7

33%

8

31%

9

18%

10

18%

11

40%

12

40%

Residual0%

The correlation parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applying to sensitivity or risk exposure pairs across different non-residual

buckets are set out in the following table:

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Bucket

1

1

2

3

4

5

6

7

8

9

10

11

12

17%

18%
22%

19%
22%

12%
14%

14%
17%

15%
18%

15%
18%

15%
18%

12%
14%

18%
22%

18%
22%

24%

14%

20%

23%

20%

19%

16%

25%

25%

16%

21%

21%

22%

19%

16%

25%

25%

23%

21%

24%

13%

17%

26%

26%

29%

30%

16%

22%

32%

32%

29%

16%

22%

33%

33%

17%

22%

33%

33%

13%

20%

20%

23%

23%

2

17%

3

18%

22%

4

19%

22%

24%

5

12%

14%

14%

16%

6

14%

17%

20%

21%

23%

7

15%

18%

23%

21%

21%

29%

8

15%

18%

20%

22%

24%

30%

29%

9

15%

18%

19%

19%

13%

16%

16%

17%

10

12%

14%

16%

16%

17%

22%

22%

22%

13%

11

18%

22%

25%

25%

26%

32%

33%

33%

20%

23%

12

18%

22%

25%

25%

26%

32%

33%

33%

20%

23%

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40%

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H.

Commodity risk

H.1

Commodity – Risk weights

61.

The risk weights depend on the commodity type; they are set out in the following table:
Bucket
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

Commodity
Coal
Crude
Light Ends
Middle Distillates
Heavy Distillates
North America Natural Gas
European Natural Gas
North American Power
European Power and Carbon
Freight
Base Metals
Precious Metals
Grains and Oilseed
Softs and Other Agriculturals
Livestock and Dairy
Other
Indexes

Risk Weight
19
20
16
19
24
24
28
42
28
53
20
19
15
16
11
53
16

62. The historical volatility ratio, HVR, for the commodity risk class is 78%
63. The vega risk weight, VRW, for the commodity risk class is 0.35

H.2

Commodity – Correlations

64.
The correlation parameters 𝜌𝜌𝑘𝑘𝑘𝑘 applying to sensitivity or risk exposure pairs within the same bucket are
set out in the following table:
Bucket
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Correlation
28%
98%
92%
97%
99%
74%
87%
35%
69%
14%
53%
63%
61%
18%
15%

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65.

16

0%

17

36%

The correlation parameters 𝛾𝛾𝑏𝑏𝑏𝑏 applying to sensitivity or risk exposure pairs across different buckets are

set out in the following table:

Buckets 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
15% 13% 17% 16% 2% 19% -2% 19% 1% 12% 12% -1% 11% 2% 0%
15%
93% 95% 93% 23% 20% 20% 20% 6% 36% 23% 30% 28% 10% 0%
13% 93%
90% 89% 15% 18% 13% 14% 2% 22% 8% 21% 13% 2% 0%
17% 95% 90%
90% 18% 22% 16% 20% 0% 35% 18% 27% 25% 5% 0%
16% 93% 89% 90%
23% 21% 20% 19% 9% 38% 25% 33% 27% 9% 0%
2% 23% 15% 18% 23%
18% 63% 16% 2% 13% -2% 18% 10% -3% 0%
19% 20% 18% 22% 21% 18%
8% 62% 11% 11% 1% 7% 10% 2% 0%-2% 20% 13% 16% 20% 63% 8%
16% -4% 9% 2% 10% 6% 3% 0%
19% 20% 14% 20% 19% 16% 62% 16%
1% 11% 0% 10% 9% 5% 0%
1% 6% 2% 0% 9% 2% 11% -4% 1%
7% 5% 7% 7% 1% 0%
12% 36% 22% 35% 38% 13% 11% 9% 11% 7%
35% 21% 20% 10% 0%
12% 23% 8% 18% 25% -2% 1% 2% 0% 5% 35%
11% 24% 5% 0%-1% 30% 21% 27% 33% 18% 7% 10% 10% 7% 21% 11%
27% 13% 0%
11% 28% 13% 25% 27% 10% 10% 6% 9% 7% 20% 24% 27%
8% 0%
2% 10% 2% 5% 9% -3% 2% 3% 5% 1% 10% 5% 13% 8%0%
0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%
9% 63% 58% 60% 62% 27% 15% 20% 13% 1% 31% 16% 35% 21% 12% 0%

Copyright © 2019 by International Swaps and Derivatives Association, Inc.

17
9%
63%
58%
60%
62%
27%
15%
20%
13%
1%
31%
16%
35%
21%
12%
0%
-

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I.

Foreign Exchange risk

I.1

Foreign Exchange – Risk weights
66. All Foreign Exchange sensitivities are considered to be within a single bucket within the FX risk class, so
no inter-bucket aggregation is necessary. Note that the cross-bucket Curvature calculations of paragraph11(d) are still required on the single bucket.

67.

The group of high FX volatility currencies is defined to be: Brazilian Real (BRL).

68.

The group of regular FX volatility currencies is defined to be all other currencies.

69.

The risk weight for a currency depends on the group of the calculation currency, as well as the group of

the currency concerned. There should be no FX risk factor for the calculation currency (or equivalently, its risk
weight should be set to zero). The risk weight for a given currency and calculation currency is given by the following
table where the row corresponds to the FX volatility group of the given currency and the column corresponds to
the FX volatility group of the calculation currency:
FX Volatility group
RegularHigh

Regular
7.57
10.28

High
10.28
10.28

70.

The historical volatility ratio, HVR, for the FX risk class is 0.65.

71.

The vega risk weight, VRW, for FX volatility is 0.30.

I.2

Foreign Exchange – Correlations

72.

The correlation parameter 𝜌𝜌𝑘𝑘𝑘𝑘 applying to pairs of FX sensitivities or risk exposures are set out in thefollowing tables. Since each FX risk factor is the exchange rate of a particular currency against the calculation
currency, the correlation between two FX risk factors depends on the FX volatility group of the two particularcurrencies as well as the FX volatility group of the calculation currency. Each table shows the correlation between
two FX risk factors, depending on the FX volatility group of each risk factor’s currency.
The first table shows the correlations between two FX risk factors if the calculation currency is in the regular FX
volatility group:
FX Volatility group

RegularHigh

Regular

50.0%

36.8%

High

36.8%

50.0%

The second table shows the correlations between two FX risk factors if the calculation currency is in the high FX
volatility group:

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FX Volatility group

RegularHigh

Regular

72.9%

50.0%

High

50.0%

50.0%

73.

For the purposes of correlating pairs of FX volatility and curvature risk factors, the correlation shall betaken to be 0.5.

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J.

Concentration Thresholds

The concentration thresholds in this section are defined for the asset-class-specific buckets specified in Sections E,
G, and H. For those cases in which the same concentration threshold applies to a related range of buckets, thetables in this section specify the precise range of applicable buckets in the Bucket column and give a narrativedescription of that group of buckets in the Risk Group column.

J.1

Interest Rate risk – Delta Concentration Thresholds

74.

The delta concentration thresholds for interest rate risk (inclusive of inflation risk) are given by currencygroup:

Currency Risk GroupHigh volatility
Regular volatility, well-traded
Regular volatility, less well-tradedLow volatility

Concentration threshold (USD mm/bp)
6.9
230
30
150

75.

The currency risk groups used in establishing concentration thresholds for Interest Rate Risk are as
follows:(1) High volatility:
All other currencies(2) Regular volatility, well-traded:
USD; EUR; GBP(3) Regular volatility, less well-traded:
AUD; CAD; CHF; DKK; HKD; KRW; NOK; NZD; SEK; SGD TWD(4) Low volatility:
JPY

J.2

Credit spread risk – Delta Concentration Thresholds

76.

The delta concentration thresholds for credit spread risk are given by credit risk group and bucket:

Bucket(s)Credit Risk Group
Qualifying
1, 7
Sovereigns including central banks
2-6, 8-12
Corporate entities
Residual
Not classified
Non-Qualifying
1
IG (RMBS and CMBS)
2
HY/Non-rated (RMBS and CMBS)
Residual
Not classified

Concentration threshold (USD mm/bp)
0.94
0.18
0.18
9.5
0.50
0.50

J.3

Equity risk – Delta Concentration Thresholds

77.

The delta concentration thresholds for equity risk are given by bucket:
Bucket(s)
1-4
5-8
9
10
11-12
Residual

Equity Risk Group
Emerging Markets – Large Cap
Developed Markets – Large Cap
Emerging Markets – Small Cap
Developed Markets – Small Cap
Indexes, Funds, ETFs, Volatility Indexes
Not classified

Concentration threshold (USD mm/%)
11
37
5.1
2.4
1,800
2.4

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J.4

Commodity risk – Delta Concentration Thresholds

78.

The delta concentration thresholds for commodity risk are given by bucket:
Bucket
1
2
3-5
6-7
8-9
10
11
12
13-15
16
17

CT bucket
Coal
Crude Oil
Oil Fractions
Natural gas
PowerFreight, Dry or Wet
Base metals
Precious Metals
Agricultural
Other
Indices

Concentration threshold (USD mm/%)
250
2,300
1,600
2,200
2,200
51
370
870
27
27
4,100

J.5

FX risk – Delta Concentration Thresholds

79.

The delta concentration thresholds for FX risk are given by currency risk group:

FX Risk Group
Category 1
Category 2
Category 3

Concentration threshold (USD mm/%)
9,100
1,600
290

80.

Currencies were placed in three categories as for delta risk weights, constituted as follows:
Category 1 - Significantly material: USD, EUR, JPY, GBP, AUD, CHF, CAD
Category 2 - Frequently traded:
BRL, CNY, HKD, INR, KRW, MXN, NOK, NZD, RUB, SEK, SGD, TRY, ZAR
Category 3 - Others:
All other currencies

J.6

Interest Rate risk – Vega Concentration Thresholds

81.

The vega concentration thresholds for Interest Rate risk are:

Currency Risk GroupHigh volatility
Regular volatility, well traded
Regular volatility, less well tradedLow volatility

Concentration threshold (USD mm)
170
2,300
190
770

82.

The Currency risk groups used in establishing concentration thresholds for Interest Rate risk are identifiedin paragraph 70 above.

J.7

Credit spread risk – Vega Concentration Thresholds

83.

The vega concentration thresholds for Credit spread risk (including the residual buckets) are:

Credit Risk Group
Qualifying
Non Qualifying

Concentration threshold (USD mm)
280
59

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J.8

Equity risk – Vega Concentration Thresholds

84.

The vega concentration thresholds for equity risk are:
Bucket
1-4
5-8
9
10
11-12
Residual

Equity Risk Group
Emerging Markets – Large Cap
Developed Markets – Large Cap
Emerging Markets – Small Cap
Developed Markets – Small Cap
Indexes, Funds, ETFs, Volatility Indexes
Not classified

Concentration threshold (USD mm)
150
1,100
40
200
9,200
40

J.9

Commodities risk – Vega Concentration Thresholds

85.

The vega concentration thresholds for Commodities vega risk are:
Bucket
1
2
3-5
6-7
8-9
10
11
12
13-15
16
17

Commodity Risk Group
Coal
Crude OilOil fractions
Natural gas
PowerFreight, Dry or Wet
Base metals
Precious Metals
Agricultural
Other
Indices

J.10

FX risk – Vega Concentration Thresholds

86.

The vega concentration thresholds for FX risk are:

FX Risk Group
Category 1 - Category 1
Category 1 - Category 2
Category 1 - Category 3
Category 2 - Category 2
Category 2 - Category 3
Category 3 - Category 3

Concentration threshold (USD mm)
290
1,500
230
2,600
900
100
390
600
680
100
270

Concentration threshold (USD mm)
3,700
1,900
640
570
390
220

87.

The Currency Categories used in establishing concentration thresholds for FX risk are identified inparagraph 80 above.

K.

Correlation between risk classes within product classes

88.

The correlation parameters 𝜓𝜓𝑟𝑟𝑟𝑟 applying to initial margin risk classes within a single product class are set

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out in the following table:
Risk ClassInterest Rate
Credit Qualifying
Credit Non-qualifying
EquityCommodity
FX

Interest Rate
27%
26%
29%
31%
14%

CreditQualifying
27%
19%
63%
42%
25%

CreditNon-Qualifying
26%
19%
19%
20%
14%

Equity
29%
63%
19%
43%
25%

Copyright © 2019 by International Swaps and Derivatives Association, Inc.

Commodity
31%
42%
20%
43%
30%

FX
14%
25%
14%
25%
30%

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Annex A: Additional Initial Formulas
Standardised formulas for calculating Additional Initial Margin are below:

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀= 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 + (𝑀𝑀𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 1)𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + (𝑀𝑀𝑀𝑀𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 1)𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶+(𝑀𝑀𝑀𝑀𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 − 1)𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + (𝑀𝑀𝑀𝑀𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 1)𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 .

Where 𝐴𝐴𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐼𝐼𝐼𝐼 is defined as:

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 + � 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑟𝑟𝑝𝑝 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑙𝑙𝑝𝑝 ,product 𝑝𝑝

Where 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 is a fixed add-on amount, 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑟𝑟𝑝𝑝 is the add-on factor for each affected product p,
expressed as percentage of the notional (e.g. 5%); and 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑙𝑙𝑝𝑝 is the total notional of the product (sum of theabsolute trade notionals). In such use, where a variable notional is involved, the current notional amount should
be used.
The four variables 𝑀𝑀𝑆𝑆𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 , 𝑀𝑀𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖𝑡𝑡 , 𝑀𝑀𝑆𝑆𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 , 𝑀𝑀𝑆𝑆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 are the four “multiplicative scales” for the four
product classes (RatesFX, Credit, Equity, Commodity). Their values can be individually specified to be more than
1.0, with 1.0 being the default and minimum value.

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