Margining Methodology on Bonds Cash and Repo
Transactions cleared by
LCH.CLEARNET SA
User’s Specifications
Version October 2011
Summary
a)
b)
Foreword .............................................................................................................. 2
Calculation of Mark-To-Market Margins ............................................................ 2
Step 1. Retrieval of market prices..................................................................... 2
Step 2. Selection of transactions to be included in calculation of Mark-ToMarket Margins .................................................................................... 3
Step 3. Calculation of the accrued coupon ....................................................... 3
Step 4. Determination of Repo interest............................................................. 3
Step 5. Determination of the Transaction Revaluated Amount ........................ 4
Step 6. Calculation of Mark-To-Market Margin per transaction...................... 4
Step 7. Calculation of the Overall Mark-To-Market Margin ........................... 4
Calculation of Initial Margins .............................................................................. 5
Step 1. Selection, evaluation and classification of transactions to be
included in Initial Margins calculation: ................................................ 5
a)
b)
c)
Selection of transactions................................................................................. 5
Transaction evaluation ................................................................................... 5
Classification of portfolio securities .............................................................. 5
Step 2. Determination of marginable positions ................................................ 5
Step 3. Calculation of non Adjusted Initial Margin.......................................... 7
Step 4. Adjusted Initial Margins ....................................................................... 7
c) Calculation of Total Margins ............................................................................... 8
d) Determination of parameters................................................................................ 8
Annex 1 - Determination of Mark-To-Market Price on MTS ITALY ...................... 9
Annex 2 - Classification and Deposit Factor ........................................................... 12
Priority and Cross Position Credit – Examples for Intra and Inter classes Priority ... 14
Annex 3 - Duration Calculation ............................................................................... 20
a) Zero Coupon Bonds ........................................................................................... 20
b) Fixed Coupon Bonds.......................................................................................... 20
c) Floating Rate Bonds ........................................................................................... 22
d) Bonds indexed on inflation rate ......................................................................... 22
Annex 4 - :EXAMPLES .......................................................................................... 23
Foreword
This document is a guide to the development of a procedure for the calculation of
margins on cash and repo (both «Classic», and «Sell-BuyBack»1) bond transactions
cleared by LCH.CLEARNET SA. This margining methodology has been implemented
since November 2002.
Besides, this methodology apply also for transactions between CC&G clearing
members and LCH.Clearnet SA clearing members on Italian Government bonds,
within the mainframe of the Interoperability link set up by these 2 CCP’s, offering the
role of Central Counterparty. Therefore, some references of this document refer to
specifications of transactions realized on MTS Italy market (reference prices).
The margining methodology foresees the following types of margins:
a)
Mark-To-Market Margins, which re-evaluate on a daily basis the portfolio to
the market;
b)
Initial Margins, which evaluate the largest possible loss under the hypothesis
of portfolio liquidation in the most unfavorable price/yield scenario reasonably
possible.
a)
Calculation of Mark-To-Market Margins
The calculation is based on the following steps:
Step 1.
Retrieval of market prices
In order to re-evaluate positions at their current market value, “mark-tomarket” prices are used; such prices are representative of market conditions
at the end of the trading day. Annex no.1 points out possible ways to
determine such prices.
French Government bonds: prices obtained at 5:30 pm CET time through a
data provider
Italian Government bonds: MTS Italy reference price: prices obtained at
4:30 pm CET time
1
The main difference between «Classic» and «Sell-BuyBack» Repos is in the management of coupons
paid during the transaction. In «Classics», coupons paid on the bond during the term of the transaction are
required to be paid on to the original seller upon receipt. Whereas in MTS «Sell-BuyBacks» coupons are
deemed to be paid to the buyer and reinvested at the repo rate until the termination of the transaction. The
coupon amount plus the interest accrued from coupon payment date to transaction settlement date is then
deducted from the cash to be received at the termination date.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 2 of 27
Spanish Government bonds: MTS reference price : prices obtained at 4:30
pm CET time
Step 2.
Selection of transactions to be included in calculation of Mark-ToMarket Margins
The following positions are included in calculation of Mark-To-Market
Margins:
Step 3.
a)
For cash transactions, all unsettled transactions as of margin
calculation date;
b)
For repo transactions, all transactions whose “cash” leg has already
been settled and its “forward” leg is still unsettled as of margin
calculation date.
Calculation of the accrued coupon
The time interval to be considered in coupon accrual calculation changes
according to the type of contract:
a)
For cash transactions, the accrued coupon is calculated starting from
the maturity date of the previous coupon until the settlement date; it is
not necessary to update such calculation during the three days between
the trade date and the settlement date given that the accrual can be
considered irrelevant for margining purposes;
b)
For repo transactions, the accrued coupon is calculated starting from
the maturity date of the previous coupon until the first working day
after margin calculation; in this case the accrual is considered relevant
for margining purposes
The accrued coupon will be calculated according to the “Euroland” market
convention (act/act).
Step 4.
Determination of Repo interest
Interests on repo transactions (RI) are calculated starting from the repo
commencement date until the first working day after margin calculation;
therefore:
RI =
t × TA × RR
36.000
where t is number of days, TA is the traded amount and RR is the repo rate.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 3 of 27
The repo interest amount is rounded to the nearest integer Euro.
Step 5.
Determination of the Transaction Revaluated Amount
The Transaction Revaluated Amount (TRA) is equal to the nominal value
(NV) of the traded security, revaluated at the current market price (P) as per
Step 1 above, plus the accrued coupon (AC) calculated as per step Step 3
above. Therefore:
TRA = (NV/100) × (P + AC)
Step 6.
Calculation of Mark-To-Market Margin per transaction
The Mark-To-Market Margin is equal to the difference between the
transaction revaluated amount as per Step 5 above and the traded amount;
for repo transactions, the repo interest amount as per Step 4 above must also
be taken into consideration.
Therefore:
a)
cash transactions:
Mark-To-Market Margin= (TRA – Traded amount) × position sign2;
b)
repo transactions:
Mark-To-Market Margin= (TRA – Traded amount – RI) × position sign.
Step 7.
Calculation of the Overall Mark-To-Market Margin
The Overall Mark-To-Market Margin is equal to the sum of all the MarkTo-Market Margins calculated for each transaction.
Overall Mark-To-Market Margins = Σ Mark-To-Market Margins per each transaction.
A negative Mark-To-Market Margin is a debit for the member towards the
CCP; a positive Mark-To-Market Margin is a theoretical credit for the
member.
2
The buyer of a cash bond has a long position (+1), and the seller a short position (-1). The holder of a
repo (sells bonds spot and buys them forward) has a long position (+1), the holder of a reverse repo (buys
bonds spot and sell them forward) has a short position (-1).
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
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b)
Calculation of Initial Margins
The methodology is based on the following steps:
Step 1.
Selection, evaluation and classification of transactions to be
included in Initial Margins calculation:
a) Selection of transactions
The following positions are evaluated (as in the case of the calculation of Mark-ToMarket Margins):
a)
For cash transactions, all unsettled transactions at margin calculation
date;
b)
For repo transactions, all transactions whose “cash” leg has already
been settled and its “forward” leg is still unsettled.
b) Transaction evaluation
In order to obtain a single net balance for each security (identified by its ISIN code),
long and short2 positions are algebraically summed (at their re-evaluated
countervalue), independently of the transaction type (cash or repo) from which they
have arisen.
c) Classification of portfolio securities
Net positions calculated at sub-step b) above are then divided in Classes, according to
their sensitivity to interest rates fluctuations. The Classes are numbered from 1 to 11
and further class (12) is used for securities (non-government debt) which are subject to
other risks (liquidity or issuer). Duration is used as an indicator of such sensitivity (see
Annex 3 - Duration Calculation).
Since duration changes every day it is necessary to reallocate daily securities in
Classes.
Annex 2 provides an example of the Duration Classes.
Step 2.
Determination of marginable positions
In order to take into consideration the opposite sensitivity to interest rate
variations of positions of different signs, positions are reduced by a
procedure that – keeping into consideration correlations between securities
sorted by Duration Classes – determines the “Marginable Positions” that is
the unbalanced positions on which margins must be calculated.
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User’s Specifications 14th October 2011
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In order to achieve such aim, a sequence of offsetting priorities is
determined according to a specific list (see 0Priority and Cross Position
Credit – Example); positions are offset within the same Duration Class
(Intra Class Priority) and subsequently among different contiguous
Duration Classes (Inter Class Priority). A Cross-Position Offsetting Factor
is associated to each Priority.
Therefore, according to the established priority sequence, long and short
positions within the same class are decremented by an amount equal to the
Cross-Position Offsetting Factor applied to the smaller of he two positions.
Decremented Long Position Class n = Long Position Class n – [priority n CrossPosition Offsetting Factor × min (Long Position Class n; Short Position Class n)]
Decremented Short Position Class n = Short Position Class n – [priority n CrossPosition Offsetting Factor × min (Long Position Class n; Short Position Class n)]
When Inter Class Priorities are considered, both the long and the short
position of one Class will be decremented of an amount equal to pertinent
Inter Class Cross-Position Offsetting Factor applied to he smaller between
the position itself and the position of opposite sign of the other Class.
Decremented Long Position Class n = Long Position Class n – [priority nm CrossPosition Offsetting Factor × min (Long Position Class n; Short Position Class m)]
Decremented Short Position Class n = Short Position Class n – [priority nm CrossPosition Offsetting Factor × min (Long Position Class m; Short Position Class n)]
Decremented Long Position Class m = Long Position Class m – [priority nm CrossPosition Offsetting Factor × min (Long Position Class m; Short Position Class n)]
Decremented Short Position Class m = Short Position Class m – [priority nm CrossPosition Offsetting Factor × min (Long Position Class n; Short Position Class m)]
For each Class the results obtained by the application of Priority n CrossPosition Offsetting Factor is the starting point for the application of Priority
n+1 Cross-Position Offsetting Factor.
Countervalues are rounded to the nearest integer euro before and after each
calculation.
Annex no.3 provides an example of a priority list.
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User’s Specifications 14th October 2011
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Step 3.
Calculation of non Adjusted Initial Margin
For each Class, long and short “Marginable Positions” – which have been obtained
through the above described procedure – are compared and the largest (in absolute
value) among them is multiplied by a coefficient (Deposit Factor) specifically
established for that Duration Class.
Unadjusted Initial Margin per Class = Class Deposit Factor × Max (Long Marginable
Position; Short Marginable Position)
The result is rounded to the nearest integer euro.
Unadjusted Initial Margins for each Duration Class are then summed up in
order to obtain the total Unadjusted Initial Margins:
Total Unadjusted Initial Margins = Σ Unadjusted Initial Margin per each Duration Class
Step 4.
Adjusted Initial Margins
Unadjusted Initial Margins as per step Step 3 above are multiplied by an
Adjustment Factor (in %), whose value can be set at member level, in order
to obtain Adjusted Initial Margins. The Adjusted Initial Margins may
support a Deposit Adjustment (in EUR amount) in specific situations.
Adjusted Initial Margins = Unadjusted Initial Margins × Adjustment Factor + Deposit
Adjustment
Adjusted Initial Margins are rounded to the nearest euro integer.
All Initial Margins are always indicated with a positive sign.
Note: in the daily html report available for clearing member information on
secured area of website, the fields are named as following:
Gross deposit = Unadjusted Initial Margins
Maj/Min rate = Adjustment factor
Deposit Adjustment = field used in case of application of a potential additional
margin, or reduction of margin in specific situations
Net Deposit= Adjusted Initial Margins
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
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c)
Calculation of Total Margins
Total Margins are equal to the sum of Mark-To-Market Margins and Initial Margins.
Should the amount Mark-To-Market Margins credit be larger than the amount of
Initial Margin debits, the difference is not paid out to the member, being just a
theoretical credit.
Total Margins = Min (Mark-To-Market Margins – Adjusted Initial Margins;0)
If Total Margins are a debit for the member, calculation of Total Margin can provide
the following results:
a)
If Total Margins are larger than the Total Margins collected the
previous day, members are compelled to deposit the difference;
b)
If Total Margins are smaller than the Total Margins collected the
previous day, the excess may be withdrawn by the member.
An Excel replication tool of Initial Margins calculation is available upon request to
LCH.Clearnet SA Account manager.
d)
Determination of parameters
The parameters used within the Margining Methodology for Initial Margin
calculations, are periodically reviewed and, if the case, updated in order to keep into
account market conditions, volatility trends and the evolution of financial instruments.
It is possible to modify:
⇒ Number of Classes;
⇒ Cross-Position Offsetting Factor;
⇒ Deposit Factor;
⇒ Adjustment Factor (at member level);
⇒ Duration Class “Borders”;
⇒ Priority List.
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User’s Specifications 14th October 2011
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Annex 1 - Determination of Mark-To-Market Price on MTS ITALY
The current price list produced by MTS SpA comprises the following prices: Highest,
Lowest and Average; the latter is calculated as a weighted average of the trades of the
whole trading day; such price may diverge from market conditions at the end of the
trading day and therefore does not appear as completely fitting as “Mark-To-Market
Price”. In order to avoid to such inconvenient it is possible to take into consideration
the following values as “Mark-To-Market Price”:
1)
Last Price;
2)
Weighted average by quantities of the prices of the last x% of traded
contracts;
3)
Weighted average by quantities of the prices of the trades executed in the
last y minutes of trading.
The Last price – being based on a single trade – may not be always representative
of general market conditions.
The weighted average by quantities of the prices of the last x% of trades has the
disadvantage of comprising – in case of scarce liquidity in the market or of activity
concentrated during the early market hours – trades executed in market conditions
which may be very different from those at market close.
The weighted average of the trades executed in the last y minutes of trading may,
always in case of scarce liquidity, comprise only a limited number of trades or even
coincide with the last price.
An efficient solution may be that of evaluating alternative solutions according to
different situations:
Case 1: the last x% of trades has been executed in the last y minutes of trading.
The Mark-To-Market price is assumed equal to the weighted average by
quantities of the prices of the last x% of traded contracts.
Case 2:
the last x% of trades has not been executed in the last y minutes of
trading:
a) If at least the z% of all trades has been executed in the last y minutes of
trading, the Mark-To-Market price is assumed equal to weighted average
by quantities of the prices of the trades done in the last y minutes of
trading;
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User’s Specifications 14th October 2011
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b) If not even the z% of all trades has been executed in the last y minutes
of trading, the Mark-To-Market price is assumed equal to weighted
average by quantities of the prices of the last z% of traded contracts.
I.e., supposing that during the whole trading day 100 contracts have been executed,
set x = 10%, y = 15 minutes and z = 5% the following cases may apply:
Case 1
20 contracts have been executed during the last 15 minutes ⇒ the last 10
contracts have been executed within the last 15 minutes: the weighted
average of the last 10 contracts will be considered;
Case 2
the last 10 contracts have not been executed within the last 15 minutes:
a)
8 contracts have been executed during the last 15 minutes (more
than z%, that is equal to 5): the weighted average of the last 8
contracts will be considered;
b)
3 contracts have been executed in the last 15 minutes (less than
z%, that is equal to 5): the average of the last 5 contracts has to be
considered.
A different solution could be to consider all the contracts traded in the day, but
applying in the calculation of the weighted average of the trades, further weights
whose amount increase progressively for each new trade up to the maximum amount
corresponding to the last trade of the day.
The algorithm to be utilized will be:
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User’s Specifications 14th October 2011
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n
P=
∑k
t −1
t =1
× ( p n−t +1 × q n −t +1 )
n
∑k
t =1
t −1
× q n −t +1
where P is the weighted average price, n the number of contracts, p1, p2,…,pn and q1,
q2,…,qn respectively the prices and the quantity of the first, second, … contract and k a
parameter variable from 0 to 1 that allows to increase (k→0) or decrease (k→1) the
weight of the trades executed later in the trading day in comparison to the earlier ones.
If k=1, the Mark-To-Market price will coincide with the Official Price (all trades have
the same weight).
In the case a bond is not traded during the whole day, the Mark-To-Market price is set
equal to the one of the previous trading day, with the proviso that CCPs may manually
change the Mark-To-Market price.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
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Annex 2 - Classification and Deposit Factor
The securities bonds are allocated in duration classes upon the Government issuer
and upon their duration.
Duration is used as the criteria of the bonds’ risk, and therefore triggers the
parameters applied for deposit calculations (i.e for Initial margins).
There are 3 bond classes, one for each debt:
-
-
-
Italian segment debt: the duration classes are numbered from 001 to 012 for
Italian bonds; class 12 is used only for all Italian Treasury bonds indexed on
inflation rate, called BTPi’s.
French segment debt: the duration classes are numbered from 101 to 113 for
French bonds; French OATi’s bonds are assigned to duration classes 101 to
111 and class 113 upon their duration
Spanish segment debt: the duration classes are numbered from 201 to 211 for
Spanish bonds
Examples of parameters tables: all parameters tables are subject to calibration
changes at any moment (for active parameters, cf. Risk Notice available on
LCH.Clearnet website)
Deposit factors applied on “Italy segment” positions:
Classes :
Italy
Duration
Duration Class
Parameter
001
(0-1 month]
0,70%
002
(1-3 month]
1,00%
003
(3-9 month]
2,40%
004
(0,75-1,25 year]
2,45%
005
(1,25-2 year]
2,50%
006
(2-3,25 year]
3,15%
007
(3,25-4,75 year]
4,20%
008
(4,75-7 year]
4,95%
009
(7-10 year]
6,65%
010
(10-15 year]
6,80%
011
(15-30 year]
15,00%
012
Italian inflation indexed
Bonds (BTPi’s)
9,00%
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User’s Specifications 14th October 2011
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Deposit factors applied on “France segment” positions:
Classes :
France
Duration
Duration Class
Parameter
101
(0-1 month]
0,45%
102
(1-3 month]
0,60%
103
(3-9 month]
1,35%
104
(0,75-1,25 year]
1,50%
105
(1,25-2 year]
1,70%
106
(2-3,25 year]
2,15%
107
(3,25-4,75 year]
3,00%
108
(4,75-7 year]
3,65%
109
(7-10 year]
4,60%
110
(10-15 year]
5,20%
111
(15-30 year]
11,05%
113
(30-50 year]
16,10%
Deposit factors applied on “Spain segment” positions:
Classes :
Duration
Duration Class
Parameter
201
(0-1 month]
0,69%
202
(1-3 month]
0,95%
203
(3-9 month]
1,90%
204
(0,75-1,25 year]
2,20%
205
(1,25-2 year]
2,40%
206
(2-3,25 year]
3,22%
207
(3,25-4,75 year]
4,40%
208
(4,75-7 year]
6,15%
209
(7-10 year]
8,53%
210
(10-15 year]
9,61%
211
(15-30 year]
17,50%
Spain
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User’s Specifications 14th October 2011
Page 13 of 27
Priority and Cross Position Credit – Examples for Intra and Inter
classes Priority
Note: These parameter’s tables are only for example, and subject to
calibration changes at any moment (for active parameters, cf. Risk Notice
available on LCH.Clearnet website)
“Italy”: minoration coefficients applied on positions on debt securities issued by Italy:
Class
001
002
003
004
005
006
007
008
001
10%
Priority 0001
002
25% 20%
Priority
0002 0012
003
20% 40% 15%
Priority
0012 0003 0013
004
15% 70% 45% 30%
Priority
0013 0004 0014 0015
005
45% 70% 50% 35%
Priority
0014 0005 0016 0017
006
30% 50% 75% 55% 45%
Priority
0015 0016 0006 0018 0019
007
35% 55% 70% 60%
Priority
008
Priority
009
Priority
010
Priority
011
Priority
012
Priority
009
010
011
012
30%
0020
0017 0018 0007 0021
45%
0022
35%
0023
45% 60% 75%
0019 0021 0008
60%
0024
45%
0025
30% 45% 60%
0020 0022 0024
75%
0009
60% 30%
0026 0027
35% 45%
0023 0025
60%
0026
80% 50%
0010 0028
30%
0027
50% 75%
0028 0011
25%
0029
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“France segment”: minoration coefficients applied on positions on debt securities
issued by France
Class
101
102
103
104
105
106
107
108
101
30%
Priority 0101
102
30% 0%
Priority
0102 0112
103
0% 45% 45%
Priority
0112 0103 0113
104
45% 85% 65% 55%
Priority
0113 0104 0114 0115
105
65% 75% 70% 60% 45%
Priority
0114 0105 0116 0117 0118
106
55% 70% 80% 65% 50%
Priority
0115 0116 0106 0119 0120
107
60% 65% 80% 65%
Priority
108
Priority
109
Priority
110
Priority
111
Priority
113
Priority
109
110
111
113
40%
0121
0117 0119 0107 0122
50%
0123
45%
0124
45% 50% 65% 80%
0118 0120 0122 0108
65%
0125
55% 50%
0126 0127
40% 50% 65%
0121 0123 0125
80%
0109
70% 60%
0128 0129
45% 55%
0124 0126
70%
0128
80% 70%
0110 0130
50%
0127
60%
0129
70% 85%
0130 0111
85%
0131
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“Spain”: applied on positions on debt securities issued by Spain
Class
201
201
Priority
202
30%
0201
Priority
203
Priority
202
203
204
205
206
25%
0202
0%
0212
0%
0212
40%
0203
0%
0213
0%
0213
207
208
70%
0204
0%
0214
0%
0215
0%
0214
65%
0205
0%
0215
209
210
211
55%
0216
45%
0217
40%
0218
55%
0216
75%
0206
60%
0219
50%
0220
45%
0221
45%
0217
60%
0219
80%
0207
65%
0222
55%
0223
45%
0224
40%
0218
50%
0220
65%
0222
80%
0208
65%
0225
55%
0226
40%
0227
45%
0221
55%
0223
65%
0225
80%
0209
70%
0228
55%
0229
45%
0224
55%
0226
70%
0228
80%
0210
65%
0230
40%
0227
55%
0229
65%
0230
85%
0211
212
213
204
Priority
205
Priority
206
Priority
207
Priority
208
Priority
209
Priority
210
Priority
211
Priority
212
Priority
213
Priority
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85%
0231
France-Italy: applied on the residual positions in spread between “France” and “Italy”
Class
101
102
103
104
105
106
107
108
001
30%
Priority 1001
002
35% 35%
Priority
1002 1012
003
30% 30% 30%
Priority
1013 1003 1014
004
30% 30% 30% 0%
Priority
1015 1004 1016 1018
005
30% 30% 25% 0%
Priority
1017 1005 1020 1022
006
0% 30% 30% 25% 0%
Priority
1019 1021 1006 1024 1026
007
0% 30% 30% 25%
Priority
1023 1025 1007 1030
008
0% 30% 25%
Priority
009
Priority
010
Priority
011
Priority
012
109
110
111
113
0%
1028
0%
1032
0%
1034
1027 1031 1008
25%
1036
0%
1038
0% 0% 30%
1029 1033 1037
30%
1009
25% 0%
1040 1042
0% 0%
1035 1039
30%
1041
25% 25%
1010 1044
0%
1043
30% 30%
1045 1011
Priority
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Italy-Spain: applied on the residual positions in spread between “Italy” and “Spain”
Class
201
202
203
204
205
206
207
208
001
30%
Priority 2001
002
25% 20%
Priority
2002 2012
003
25% 20% 20%
Priority
2013 2003 2014
004
20% 20% 45% 0%
Priority
2015 2004 2016 2018
005
15% 50% 70% 0%
Priority
2017 2005 2020 2022
006
0% 50% 70% 70% 0%
Priority
2019 2021 2006 2024 2026
007
0% 65% 70% 70%
Priority
2023 2025 2007 2030
008
0% 65% 70%
Priority
009
Priority
010
Priority
011
Priority
012
209
210
211
0%
2028
0%
2032
0%
2034
2027 2031 2008
70%
2036
0%
2038
0% 0% 65%
2029 2033 2037
70%
2009
65% 0%
2040 2042
0% 0%
2035 2039
55%
2041
60% 60%
2010 2044
0%
2043
50% 65%
2045 2011
Priority
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 18 of 27
France-Spain: applied on the residual positions in spread between “France” and
“Spain”
Class
201
202
203
204
205
206
207
208
101
30%
Priority 2101
102
25% 25%
Priority
2102 2112
103
25% 20% 20%
Priority
2113 2103 2114
104
20% 20% 20% 0%
Priority
2115 2104 2116 2118
105
20% 25% 30% 0%
Priority
2117 2105 2120 2122
106
0% 25% 30% 30% 0%
Priority
2119 2121 2106 2124 2126
107
0% 25% 25% 30%
Priority
2123 2125 2107 2130
108
0% 25% 25%
Priority
109
Priority
110
Priority
111
Priority
113
209
210
211
0%
2128
0%
2132
0%
2134
2127 2131 2108
25%
2136
0%
2138
0% 0% 25%
2129 2133 2137
25%
2109
30% 0%
2140 2142
0% 0%
2135 2139
20%
2141
25% 30%
2110 2144
0%
2143
25% 30%
2145 2111
Priority
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 19 of 27
Annex 3 - Duration Calculation
a)
Zero Coupon Bonds
The duration is, by definition, equal to the maturity of the bond.
b)
Fixed Coupon Bonds
The duration or Macaulay’s Duration (D) of a fixed coupon bond producing n cash
flows f1, f2,…f5,…fn at the maturities t1, t2,…t5,…tn which may be reinvested at rate i, is
represented by the following analytic expression:
n
D=
∑ t f (1 + i )
s =1
n
s
−t s
s
∑ f (1 + i )
−t s
×
1
v
s
s =1
Description of variable:
⇒ n is the number of the future cash flows (coupons and principal);
⇒ v is the annual frequency of coupons payments (i.e. 2 if semiannual);
⇒ ts is the number of periods (or fraction) between the calculation date and the
maturity day of fs;
⇒ fs is the amount of the periodical cash flow; it is equal to the coupon times the
nominal value of the security, the last cash flow includes the principal,
which is equal to the nominal value of the bond itself;
⇒ i is the internal rate of return (IRR); the IRR is the discount rate that when
applied to futures cash flows produces the current market value of the bond.
It is obtained by solving iteratively the following equation:
n
∑ f (1 + i )
s =1
−t s
s
=P
where P is the current market value of the bond (dirty price).
All figures are rounded to the fourth decimal.
Below is an example of the duration at September 28, 2011 (settlement date
September 29, 2011) of a BTAN (Isin FR0117836652), final maturity January 15,
2015, annual coupon of 2.5%, and annual payout.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 20 of 27
date
t (in
period)
Cash flows
(f)
Discounted cash
flows f(1+i)-t
t
X
discounted cash
flows f(1+i)-t
Calcuation
28 Sept 2011
First coupon
15 Jan 2012
0.2957
2.5
2.4900
0.7363
Second coupon
Third coupon
15 Jan 2013
15 Jan 2014
1.2977
2.2971
2.5
2.5
2.4565
2.4236
3.1879
5.5671
Forth coupon +
principal
15 Jan 2015
3.2964
102.5
98.0328
323.1525
Sum
105.4029
332.6438
Duration
3.1559
The duration is equal to 3.1559 years (3 years and 57 days); the discount rate (IRR) is
equal to 1.361% per annum; it has been derived from the bond dirty market price
(105.4053) on September 28, 2011.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 21 of 27
c)
Floating Rate Bonds
Macaulay’s duration is not applicable to floating rate bonds. The price volatility of
these bonds is very low; in fact – since future coupons are adjusted to market rates –
in case of a drop (raise) of interest rates, gains (losses) on the capital account are offset
by losses (gains) on the interest receivable account.
However such realignment of the bond price to market rates conditions is not perfect
valid for CCTs, since the accruing coupon is predetermined and its non-variability has
necessarily an impact on the price of the bond (so-called “rigidity effect”), that will
therefore show small variations in case of variations of interest rates3.
The duration model for floating rate bonds are often too complex to be a viable
solution for operational applications. The duration of floating rate bonds can be
reasonably assumed equal to the time to maturity of the accruing coupon (t1)4.
d)
Bonds indexed on inflation rate
BTPi : All Italian inflation indexed bonds are considered into class 012 whatever their
duration.
OATi: These French inflation indexed bonds are assigned to duration classes 101 to
111 and class 113 upon their real duration.
3
4
The coupon is equal to 6 months gross RendiBot determined at the last auction before the beginning of
the coupon accrual period plus a spread (s, equal to 0.30 or 0.15).
The complete modified duration formula (which takes into consideration also the spread s) for a floating
rate bonds is the so-called Yawitz’s Duration:
Df =

t1
( s − fm)[1 − (1 + i ) − n ] 1 + i
n
+
×
−
n
(1 + i )
P×i
(1 + i ) − 1
 i
This formula takes into consideration both the already mentioned “rigidity effect” and the “rental effect”
that is given by the difference between the spread (s) and the financial margin (fm), which represents the
additional cost (compared to market yields) applied by the market to floating rates bonds.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA
User’s Specifications 14th October 2011
Page 22 of 27
Annex 4 - :EXAMPLES
Disclaimer: This calculation tool has been created by LCH.Clearnet SA to assist current and potential clearing members in order for them to estimate their variation margin
on the Fixed Income segment cleared by LCH.Clearnet SA. LCH.Clearnet SA does not warrant or represent that this calculation tool is comprehensive, complete, verified or
accurate and accepts no responsibility or liability for any loss, damage, cost or expense of whatsoever kind arising directly or indirectly from or in connection with the use
of this calculation and accepts no liability for decision taken, or systems work carried out by any party, based on this calculation tool. This calculation tool does not form
part of the Clearing Rules or any contractual documentation between LCH.Clearnet SA and its clearing members.
1.
Sample calculation of variation margin
Given the following portfolio on 03/12/2010 for value on 06/12/2010:
Securities
ISIN Code
Currency
Duration class
Trade date
Commencement
date
Settlement date
of the first leg
Return date
/delivery date
(cash trade)
Repo Rate
Rate type
Transaction type
Side of the
market
Face value
Traded amount
REPO trades
3
4
OBL 8,7% 2 BON 2,3% 30/
8/02/2012 20
04/2013 206
4
ES000001159 ES00000121T
5
5
1
BTP 01/02/20
15 4.25% 007
2
OAT 4% 25/0
4/2018 0087
IT000371991
8
FR001060498
3
EURO
007
30/07/2009
01/06/2010
EURO
108
14/06/2010
16/06/2010
EURO
204
30/11/2010
03/12/2010
01/06/2010
16/06/2010
31/05/2011
CASH trades
2
3
OAT 4% 25 A BTP 15/12/20
VRIL 2055 011
12 2.0% 005
5
OBL 8,7%
28/02/2012
6
BON 2,3% 30/
04/2013 206
1
OAT 4% 25/0
4/2018 0087
ES0000011595
ES00000121T5
FR001060498
3
FR0010171975
IT000456463
6
IT000349325
8
EURO
206
30/11/2010
01/12/2010
EURO
204
02/12/2010
06/12/2010
EURO
206
29/11/2010
30/11/2010
EURO
008
02/12/2010
EURO
111
02/12/2010
EURO
005
02/12/2010
EURO
008
01/12/2010
03/12/2010
01/12/2010
06/12/2010
30/11/2010
16/06/2011
06/12/2010
08/12/2010
08/12/2010
03/12/2010
07/12/2010
07/12/2010
07/12/2010
06/12/2010
1.555
FORFEIT
Repo
Send
0.5
FIXED
Repo
Take
0.30
FORFEIT
Buy/sell back
Send
0.32
FORFEIT
Buy/Sell back
Take
0.31
FORFEIT
Fwd
Take
0.65
FORFEIT
Fails (suspens)
Send
CASH
Sell
CASH
Buy
CASH
sell
CASH
buy
25 000 000
26 162 210
5 000 000
4 463 493.15
25 000 000
100 000 000
113 712 600
100 000 000
102 855 342.47
5 000 000
5 522 835.60
5 000 000
5 399 335.60
10 000 000.
10 385 628
10 000 000
10 416 671
200 000 000
226 454
602.74
24 473
698.63
(*) : Buy/Sell back =Buys bonds spot and sells them forward
(**) : Repo/BSB Take = Securities buyer and cash provider
(***) : Repo/BSB Send = Securities seller and cash receiver
4
BTP 01/02/20
19 4,25 % 008
I) Calculation of variation margin
1) Step 1: Retrieval of settlement prices
In general, settlement prices are set based on the following sources:
OATs =>
Prices provided by INTERACTIVE DATA
BTPs => Prices provided by MTS
OBL and BON =>
Prices provided by MTS
Securities
BTP 01/02/2015 4.25% 007
OAT 4% 25/04/2018 0087
OBL 8,7% 28/02/2012 204
BON 2,3% 30/04/2013 206
OAT 4% 25/04/2018 0087
OAT 4% 25 AVRIL 2055 011
BTP 15/12/2012 2.0% 005
BTP 01/02/2019 4,25 % 008
ISIN
IT0003719918
FR0010604983
ES0000011595
ES00000121T5
FR0010604983
FR0010171975
IT0004564636
IT0003493258
Settlement prices, 03/12/2010 end-of-day
103.78
107.5
107.092
97.92
107.73
104.03
99.29
101.09
2)
Step 2: Selection of transactions included in the calculation of the variation margin
The whole Repo + Cash portfolio is subject to calculation of the regular variation margin, except for:
• Forward repo (OBL 8,7% 28/02/2012) for which a specific margining has to be calculated;
• Net fails (BON 2,3% 30/07/2013) for which a specific margining and penalty rate has to be calculated.
3)
Step 3: Calculation of accrued coupon
- For cash trades, the accrued coupon is calculated from the last coupon date to the settlement/delivery date.
For the calculation of the variation margin, there is no need to revalue the accrued coupon.
- For repo and buy/sell back trades, the accrued coupon is calculated from the last coupon date to the first
business day following the calculation date (generally D+1), i.e. 06/12/2010 in this example.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA User’s Specifications 14th October 2011
Page 24 of 27
Trades
BTP 01/02/2015 4.25% 007 - Repo
OAT 4% 25/04/2018 0087 - Repo
OBL 8,7% 28/02/2012 204- Buy/sell back
BON 2,3% 30/04/2013 206- Buy/Sell back
OAT 4% 25/04/2018 0087 – Buy
OAT 4% 25 AVRIL 2055 011 - Buy
BTP 15/12/2012 2.0% 005 - Buy
BTP 01/02/2019 4,25 % 008 - Sell
4)
Revalued coupon on 06/12/2010
(Repo or buy/sell back)
1.466712
2.465753
6.69231
1.37875
Coupon on settlement/delivery date
(cash trades)
2.476712
2.465753
0.95
1.466712
Step 4: Calculation of repo interest (interest on cash amount exchanged)
Repo interest is calculated as follows:
Number of days
Traded amount
x
Repo rate x
---------------------------------------- / 100
360
The repo interest amount is rounded to the nearest whole EURO.
Trades
BTP 01/02/2015 4.25% 007 – Repo
OAT 4% 25/04/2018 0087 – Repo
OBL 8,7% 28/02/2012 204- Buy/sell back
BON 2,3% 30/04/2013 206- Buy/Sell back
5)
Traded amount
Repo rate
Number of days
Repo interest, calculated on
06/12/2010
26 162 210.00
4 463 493.15
226 454 602.00
24 473 698.75
1.555
0.50
0.30
0.32
188
173
3
5
212 452
10 725
5 661
1 088
Step 5: Calculation of the traded revalued amount
The traded revalued amount is equal to the face value of the trade revalued at the settlement price plus the accrued
coupon calculated in Step 3.
- a) For cash transactions:
- Traded revalued amount = face value x (03/12/2010 End-of-day settlement price + accrued coupon used to
calculate the traded amount) / 100
- b) For repo transactions:
Traded revalued amount => face value x (03/12/2010 End-of-day settlement price + accrued coupon to
06/12/2010) / 100
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA User’s Specifications 14th October 2011
Page 25 of 27
Trades
Transaction
type
Nominal
BTP 01/02/2015 4.25% 007
OAT 4% 25/04/2018 0087
OBL 8,7% 28/02/2012 204
REPO
REPO
BSB
BON 2,3% 30/04/2013 206
OAT 4% 25/04/2018 0087
OAT 4% 25 AVRIL 2055 011
BTP 15/12/2012 2.0% 005
BTP 01/02/2019 4,25 % 008
BSB
CASH
CASH
CASH
CASH
25 000 000
5 000 000
200 000
000
25 000 000
5 000 000
5 000 000
10 000 000
10 000 000
6)
Traded amount
Reappraised
price
Reappraised Coupon
Traded revalued
amount (Repo/BSB)
26 162 210.00
4 463 493.15
226 454 602.00
103.78
107.5
107.092
1.466712
2.465753
6.69231
26 311 678.00
5 498 287.65
227 568 620.00
24 473 698.75
5 522 835.60
5 399 335.60
10 385 628.00
10 416 671.00
97.92
107.73
104.03
99.29
101.09
1.37875
2.476712
2.465753
0.95
1.466712
24 824 687.50
Traded revalued amount
(Cash trades)
5 510 335.60
5 324 787.65
10 024 000.00
10 255 671.20
Step 6: Calculation of the variation margin per transaction
Variation margin on repo/bsb
called on 03/12/2010 at end of day
1) Send REPO/BSB => Collateral provider :
Variation margin = (- traded amount) + (traded
amount revalued at end-of-day settlementprice) (repo interest)
2) Take REPO/BSB => Collateral receiver
Variation margin = (traded amount) - (traded amount
revalued at end-of-day settlementprice) + (repo
interest)
Variation margin on cash trades
called on 03/12/2010 at end of day
1) Securities purchases
Variation margin = (- traded amount) + (traded amount
revalued at end-of-day settlement price)
2) Securities sales
Variation margin = (traded amount) - (traded amount
revalued at end-of-day settlement price)
Note: The repo interest amount is included in the margin calculation, debited from the margin of the counterpart who holds the cash and credited to
the margin of the counterpart who provided the cash.
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA User’s Specifications 14th October 2011
Page 26 of 27
Trades
Side of the Market
BTP 01/02/2015 4.25% 007
OAT 4% 25/04/2018 0087
OBL 8,7% 28/02/2012 204
BON 2,3% 30/04/2013 206
OAT 4% 25/04/2018 0087
OAT 4% 25 AVRIL 2055 011
BTP 15/12/2012 2.0% 005
BTP 01/02/2019 4,25 % 008
7)
Send
Take
Send
Take
Buy
Buy
Sell
Buy
Variation margin called
on repo transactions
Debit
Credit
134 145.75
1 033 925.92
964 935.89
136 451.15
Variation margin called
on cash transactions
Debit
Credit
12 500
74 547.95
361 628.00
160 999.80
Step 7: Calculation of the total variation margin
The total variation margin called is equal to the sum of the variation margins of all cash-trade buy/sell transactions
and repos.
TRADES
REPO/BSB
CASH
TOTAL
To be debited
To be credited
964 935.89
235 547.75
1 304 522.92
374 128.00
1 200 483.64
1 678 650.92
The total variation margin calculated on 03/12/2010 - value 06/12/2010 is as follows:
Variation margin in EURO (Repo + Cash) = 478 167.28
Margining Methodology on Bonds Cash and Repo Transactions cleared by LCH.CLEARNET SA User’s Specifications 14th October 2011
Page 27 of 27