Variance Futures on Eurex Exchange
Product description & clearing concept
Variance Futures on Eurex Exchange
Content
• Product description
• Clearing concept
• Appendix
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2
Variance Futures on Eurex Exchange
Outline
Challenge:
• Swap products difficult to capture via futures ßà transaction based settlement required
• Product needs to be tradable any day and mimic the pay off profile of a Variance Swap
Solution:
• Futures concept moves individual transactions into a standard product
à like EURO STOXX 50® Index futures
• Variance Futures with a standard variance strike, fixed start date and expiration
• At the end of the trading day all transactions are settled towards the standard futures
• Traded in notional Vega and volatility
• Converted into Variance Futures and settled in variance
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3
Variance Futures on Eurex Exchange
Market snapshot
notional Vega
volatility strike
Bloomberg
VETA <INDEX> CT
thomsonreuters
<0#EVAR:>
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4
Variance Futures on Eurex Exchange
Vega to Variance – Vola Strike to Futures Price
• During the day, the product trades in notional Vega at volatility strikes
• On trade match, the notional Vega of the trade will be converted into a position in Variance Futures and
the traded volatility strike will be converted into a Futures price, HOW:
• First, the traded volatility strike is converted into variance and adjusted for the historical variance of the
(running) standard Futures:
2
∗
=
−
+
∗
• The traded strike will now be converted into the standard Futures:
∗
=
−
∗
−
∗
+
(C**)
• The notional Vega will be converted into Variance Futures, also adjusted for the history of the (running)
standard Futures. The amount is dependent on the traded price
=
2∗
(
∗
) (
−
( )
( ))
Variance Futures are implemented using T= amount of Variance observations
TVariance Futures=(Total Days-1)Variance Swap
* Discount Factor and Accumulated Return on Modified Variation Margin (ARMVM)
account for NPV effects when buying into an existing contract
** The constant keeps the Futures price out of negative territory
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5
Variance Futures on Eurex Exchange
NPV effects
• Accumulated return on modified variation margin (ARMVM) is defined as:
=
∗
(
∆
)
+(
− )∗(
( (
∆
)
-1)
– The second term captures the daily cost of carry of the economic value of the swap. This represents the cost of
carry of margin payments as the initial value of a swap is zero and hence the price of the (non) standard futures is
zero. Therefore, the constant has to be removed, as well
à At first trading day of the standard futures contract ARMVM = 0
– The first term compounds this daily cost of carry over time
– ARMVM aligns the OTC P&L with the Variance Futures P&L:
OTC
Variance Futures
(realized variance – variance strike)
(realized variance – variance strike) – carry profits
from variation margin payment + carry losses from
variation margin payments
ARMVM
• The discount factor “NPVs” the expected value of the “standard” swap between today and maturity
=
(
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)
6
Variance Futures on Eurex Exchange
Illustration
time to maturity
0
T
t
realized variance
ST =
realized
variance
Ft =
implied 2
volatility
0
t
-
standard strike
-
standard strike
0
T
-
1-D
-
T
t
ARMVM
ARMVM
The cumulative cash flow at final settlement day will be:
realized
variance
ST
-
Ft
=
standard strike
-
implied 2
volatility
standard strike
+
1-D
ARMVM
ST final settlement price of the futures
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Ft traded futures price in “t”
7
Trade Example
Trade in an OTC Variance Swap on 30
May 2016
• 100,000 Vega at 22.68% volatility
– Settlement on 19 August 2016
– 2,205 Variance units
– 514.38 Variance strike
Trade in Variance Futures on 30 May
2016
• 100,000 Vega at 22.68% volatility
– 2,391 AUG16 Variance Futures
– at a price of 2,974.9939
The Futures:
– SX5E at 3,090.01
•
Total life time : 64 variance
observations
•
Accrued variance observations : 5
•
Remaining life time: 59 variance
observations
•
Standard strike : 23.20%
• At settlement on 19 August 2016:
Final settlement price = 3,208.0365
• At settlement on 19 August 2016:
– Final realized Variance: 766.94 (27.69% volatility)
– Equity amount: (766.94 – 514.38) * 2,205 =
556,774.50€*
Cumulative variation margins:
(3,208.0365 -2,974.9939) * 2391
=
557,301.53
+ Cumulative ARMVM
(ARMVM T – ARMVM t) * 2,391
– SX5E at 2,970.53 (12:00 EDSP)
=
-490.86**
- Discount of the “standard” swap in t: (1-D t)*(traded
variance – standard strike) * number of futures
=
Total P&L:
=
36.18**
556,774.49€*
»The difference between implied and realized volatility of 5.01% points results into a 557K € profit
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*P&L is calculated using non-rounded amounts of futures/ variance units
** Negative interest rates create inverse NPV effects
8
Standardization & Fungibility (1/2)
• Variance Futures are standardised in two dimensions:
– Maturity: Variance Futures will have the same maturities as the related Options products
– Variance Strike: Each Maturity will have a standard variance strike that is set on the first trading day
based on market level
• Each individual trade will be converted into a position in the standard Variance Futures contract with the
respective maturity:
– The economics of the spot starting Variance Swap are converted into a Futures with a history
– The traded Volatility strike is converted into the standard Volatility (variance-) strike of the Futures
• Variance Futures are fully fungible and can be traded in and –out at any point during their life time
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Standardization & Fungibility (2/2)
• Trading and Clearing in different notations involves conversions from Vega to Futures and from
volatility strikes to Futures prices
• Variance Futures Prices contain two major elements:
– The realized variance from the start day of the contract until the trade day
– The implied variance resulting from the traded volatility strike
• In order to replicate a Variance Swap trade that starts with the first underlying price observation at the
end of the trading day, trades need to be converted twice from volatility to Futures prices:
1.
Intraday after a trade match: à into PRELIMINARY Futures prices
2.
End of day: à into FINAL Futures prices that include the realized variance until the end of the
trading day
•
At Eurex, these conversions are done by the Trading System “T7”
•
Matched trades are reported to the clearing system in Futures only; the clearing and position keeping
takes place in Futures only
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10
Variance Futures on Eurex Exchange
Comparison: Variance Futures vs. Variance Swap
• The Variance Futures yield the same P&L like the equivalent OTC Variance Swap:
1.
Buy futures on first trading day and hold until maturity
2.
Buy futures after first trading day at market price level and hold to maturity
• In the following trade scenarios the P&L in Variance futures may differ from the equivalent OTC P&L:
1.
Buy futures on first trading day and sell prior to expiry at market price level
2.
Buy futures after first trading day at market price level and sell prior to maturity at market price
level
à Compared to an early terminated Variance Swap, the Variance Futures that is sold before maturity
includes the EURO STOXX 50® price point at the end of the day of the termination
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11
Variance Futures on Eurex Exchange
Summary
• The Variance Futures converts the pay off streams resulting from different OTC Variance Swap
transactions and convert them into a (uniform) pay off stream resulting from a standardized product
using daily margining
• The standardization creates fungibility
• Selling the contract before maturity adds an additional price point to the final realized variance. Other
than the OTC convention the closing of the position includes the EURO STOXX 50® price at the end of
the trading day into the calculation of the realized variance
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12
Variance Futures on Eurex Exchange
Product details
Price conversion
On-exchange trades are converted twice:
1.
Upon matching from volatility into a preliminary futures
price
2.
End of day into the final traded futures price. This factor in
the realized variance until end of day (starts the variance
observation at the end of the trading day)
3.
On the first trading day trade matches are generally
converted to a futures price of 3000, intra day. The first
conversion according to the formulas takes place end of
day
Standard strike
The standard strike will be determined on the first trading day and
be equal to the settled implied volatility »1st settlement price in
the futures = 3000
Interest rates
•
•
Market disruption event
ARMVM will be calculated using the EONIA rate, settled at
19:00 CET on the previous day
The discount factors are calculated using EURIBOR rates,
fixed at 11:00 CET and interpolated to the respective maturity
of the futures (see backup for the interpolation formula)
1) STOXX® fails to provide an index closing level
2) Eurex Exchange fails to open for trading during scheduled
trading hours
3) Other market disruption events according to the European
OTC standard
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13
Variance Futures on Eurex Exchange
Contract specifications – Overview
EURO STOXX 50® Variance futures (EVAR)
Contract value
1 € per Variance Futures point
Contract terms
Variance Futures are available for trading at Eurex Exchange until one day before the final settlement day
of each of the following terms: up to and in each case including the final settlement day of the next, the
second and the third succeeding calendar month and the next three succeeding quarter-end months
(March, June, September, December) and the next two succeeding half-year expiration days (June and
December) thereafter
Minimum price change
0.0001 Variance Futures points
Tick value
0.0001 €
Settlement
Cash settlement
Final settlement price/ expiration
day
Based on the average of the EURO STOXX 50® index calculations between 11:50 until 12:00 CET on
the third Friday of the maturity month
Final settlement day
Next trading day following the last trading day
Last trading day
One business day before the third Friday of the maturity month
Continuous trading
09:00 – 17:30 CET
Eurex Trade Entry Services
9:00 – 21:00 CET
Eurex Trade Entry Services
minimum size
1 contract
Trading calendar
Variance Futures will be tradable on each Eurex trading day. The maturing contract month will not be
tradable on its maturity day
• Variance Futures are traded on-exchange in terms of notional vega at volatility. Upon matching
notional vega and volatility are converted into Variance Futures at Variance Futures prices. The
corresponding conversion formulas and parameters are published by the exchange.
• Block trades are entered in Variance Futures at FINAL Variance Futures prices
Trade matching/ Block Trade Entry
Service
Order maintenance
•
•
•
Notional vega at volatility
Minimum order size = 1 vega
Minimum price change = 0.05 volatility points
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14
15
Margining in Variance Futures
Margin requirement for Variance Futures
-Initial margin per 100K Vega-
Product
Series
Size
OESX
MAR17 2950
Put
3.000 long
OESX
MAR17 3500
Call
1.500 long
EVAR
MAR17
17.510 short
Vega
~100.000 long
~ 100.000 short
EuroStoxx options hedged with Variance Futures
-Initial margin, separate and combined-
88 % margin reduction
• Variance Futures are portfolio margined with
• EuroStoxx 50® options
• VSTOXX® Futures
• Options on VSTOXX® Futures and VSTOXX®
options
• Vega offsetting positions can generate substantial
margin efficiencies
Margin calculations as of 28 December 2016
~ 3 months to maturity
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Variance Futures on Eurex Exchange
Content
• Product description
• Clearing concept
• Appendix
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16
Variance Futures on Eurex Exchange
Clearing concept – Overview
• In order to replicate the pay-off profile of an OTC Variance Swap the conversion from vega to futures
has to take place at the end of the day, when the EURO STOXX 50® closing price is available
• Intraday, Eurex Exchange converts order book trades from vega to futures at a preliminary futures price
• End of day, the preliminary trades are replaced by trades based on the original vega notional and
volatility strikes, but with a futures price that considers the EURO STOXX 50® close in its realized
variance
• The futures quantity will not change between intraday and end of day
• The method to replace the futures price end of day is PRELIMINARY/Rebook
• Trade- and position adjustments can be done also based on PRELIMINARY futures prices. The end of
day price update will follow
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Preliminary Prices Handling
Trade Acceptance
T7
C7
EoD
Preliminary Prices in T7
Final Prices in T7
Participants
Participants
TradeCapture
Report
TradeCapture
Report
Preliminary Prices in C7 marked with a Preliminary Price Tag
Automatic
inverse booking
of the Preliminary
Price and rebooking of the
Final Trade with
the Final Price
Final Prices in C7
Definition
Booking Logic
The preliminary priced transactions receive their final price EoD
from T7. The update is processed as booking-out of the preliminary
priced transaction and booking-in of the transaction with final price
The transactions with preliminary price will be automatically
adjusted when the final price is received from T7
Trade Entry Service
The price adjustment is position neutral. Thus, all position
adjustments are allowed for preliminary priced transaction
After TES Migration preliminary priced off-book transactions will
be handled as all on-exchange transactions
The transaction with final price does not carry preliminary price tag
Preliminary priced transactions are available for transaction
adjustments (excluding average price adjustment)
All adjustments on preliminary price transactions carry the
preliminary price tag until the final price adjustment takes place
Pending give-ups will be reinstated after final price adjustment
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18
Variance Futures on Eurex Exchange
Summary: Transaction processing in the Eurex Clearing system
Preliminary transaction
Booking out
Booking in
Timing
- Intraday
- End of day
- End of day
Quantity/
price
- futures quantity
- INTERIM futures price
- Original transaction is
AUTOMATICALLY adjusted
- No changes to the quantity
- FINAL futures price resulting from the
end of day conversion
Required
flag/ID
- Order ID (containing the T7
Order ID)
- Time stamp of the original
trade
- The transaction is
ADJUSTABLE
- Order ID (containing the T7
Order ID)
- Time stamp of the book-out
transaction
- Order ID (containing the T7 Order ID)
- Time stamp of the final trade
- The new transaction will contain the
Eurex Original Order ID (containing the
T7 Order ID)
- The transactions can be linked in the
Eurex Clearing GUI by the T7 Order ID
Confirmation
/messages
- Real time transaction
confirmation from the clearing
system with futures quantity
and INTERIM futures price
- The transaction will be
marked to indicate it is
preliminary
- The message will indicate
the preliminary transaction to
be booked out
- Transaction confirmations from the
clearing system will be sent again in
futures with FINAL futures prices
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19
Variance Futures on Eurex Exchange
Trade Capture Report (TCR): Attributes
Preliminary
Trade
Booking out
Booking in
Comment
4 = Cleared with preliminary price
Cleared
Indicator
4
4
0
Secondary
Order ID
---
---
---
1230000000000
1230000000001
1230000000002
Transaction
Type
0
13
13
Free Text 1
---
---
---
1) C
2) O
C
O
C
O
Trade Report
ID
From C7 Release 3.0, only order ID field will be
used as unique identifier for order.
SecondaryOrderID is removed. (DFS9121)
C7 key identifier for transactions: Transaction ID
+ Suffix
(Transaction ID)
Field TransferReason. Eurex internal transaction
type.
0 = TRADE
13 = TRADE_PRICE_ADJUSTMENT
Usage of Free Text field for marking
PRELIMINARY or FINAL transaction is
discontinued.
•
Position Effect
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•
•
Preliminary trades will be booked with original
position effect at Eurex Clearing;
Example 1): Original trade executed to „close“
Example 2): Original trade executed to „open“
20
Variance Futures on Eurex Exchange
Regulatory reporting
• BaFin requires the reporting of the final booking with:
– The price of the final booking
– The time stamp of the final booking
• Eurex Exchange will only report the final booking to BaFin;
preliminary and the cancellation booking will not be reported
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21
Variance Futures on Eurex Exchange
Time axis
Pre trading
18:30 CET: final
conversion
parameters available
Trading
9:00 – 17:30
Post Trading
Full
17:30 – 21:00
Post late 1
Post late 2
Post restricted
22:00
• Pre-Trading
– Enter quotes and orders
• Trading
– Order book and TES trades are handled with PRELIMINARY futures prices
– Full support of trade adjustments
• Post-Trading Full
– Addition of EURO STOXX 50® close price to the realized variance
– Calculation of final conversion parameters
– Cancellations
– Re-bookings
– Enter quotes and order for following day
– Availability of post trade functions
– TES trades until 21:00
• Post-late 1
– No Eurex Trade Entry Services
• Post-late 2
– Only cancellation of pending Give up’s is possible
– No Take up possible
• Post-Trading restricted
– Only data inquiries
– And entry of order for following day
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22
Variance Futures on Eurex Exchange
Content
• Product description
• Clearing concept
• Appendix
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23
Variance Futures on Eurex Exchange
Appendix
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24
Variance Futures on Eurex Exchange
Special – First trading day of a new contract
• On the first trading day of a new contract month there are no conversion parameters from the previous
day that can be used for the preliminary conversion, intraday
• The futures starts with
– ARMVM = 0
– Realized variance (σ2realized) = 0
• Using settled implied volatility at the end of the day = standard strike for the new contract month creates
a starting point of the new futures of 3000:
=
∗
−
∗
=0
∗
−
+
=0
• The preliminary prices that are matched during the day will all be set to 3000, the settlement price in the
futures
• During the end of day conversion, the final trade prices will be calculated, using the settlement volatility
as a standard strike
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25
Variance Futures on Eurex Exchange
Special ‒ Last trading day & maturity
• The futures settles the last time against the EURO STOXX 50® final settlement price at 12:00 CET on
the third Friday of the maturity month
• On that day, trading in the futures will NOT be possible, because:
– The equivalent Variance Swap would start and end with the same price point
– The quantity conversion from vega to futures would lead to an error:
=
2∗
(
∗
) (
−
( )
( ))
=0
• Note there will be no trade/position adjustments possible until Post-Trading Full phase
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26
Variance Futures on Eurex Exchange
Rounded
to the
nearest
integer
Trades at different prices on 1st trading day
vol strike
vega '000
implied vol
(spot to
par
realized var exp)/
from trade settlement variance
price
strike II
date
Accrued
Days
Date
0
0
1
2
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
49
50
51
52
53
54
55
56
57
58
59
66
67
0 trade price
0 0,21682311
519,789398 0,21640587
340,809657 0,22212112
382,53721 0,19621375
359,977417 0,19262792
396,249202 0,2062687
501,44077 0,22958348
478,257925 0,23808835
461,485493 0,22907646
445,134157
0,239214
430,534054 0,24350283
456,859287 0,26611205
456,354515 0,25332027
471,405579 0,24093684
497,260589 0,21726617
479,219926 0,20675891
472,443635 0,2213593
455,68207 0,21882953
1047,01007 0,38390993
1030,98539 0,40937651
1017,7874 0,39608444
1021,79994 0,35586809
1002,52094 0,34832241
1019,81743 0,32101765
1001,39156 0,32692887
1047,04262 0,37222066
1150,24199 0,47486604
1137,72737 0,47524843
1166,63876 0,41575606
1250,1646 0,36197018
35,3576668
470,122601
469,094925
488,75466
384,476289
368,537501
418,384488
520,480215
542,696237
506,5448
533,718466
541,26284
624,3906
577,117472
540,832881
481,596919
447,869958
482,817499
469,029036
1156,95841
1187,3262
1143,0241
1073,68926
1044,03508
1021,76395
1012,63044
1098,32134
1300,88774
1273,59201
1226,2334
1250,1646
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
discount factor ARMVM
0,994971589
0,994971589
0,99502611
0,995189689
0,996062567
0,996117147
0,99617173
0,996335498
0,996390093
0,996444691
0,996499292
0,996553897
0,996717727
0,996772343
0,996826963
0,996881585
0,99693621
0,997100103
0,99715474
0,99874052
0,998795247
0,998849977
0,999014185
0,999068927
0,999123672
0,99917842
0,999233171
0,999397442
0,999452205
0,999506971
1
Future price w/ TVA
0,0000
0,0000
0,0000
-0,0002
-0,0107
-0,0154
-0,0209
-0,0294
-0,0267
-0,0227
-0,0207
-0,0172
-0,0056
0,0028
0,0087
0,0125
0,0132
0,0095
0,0102
0,7558
0,7934
0,8326
0,9431
0,9762
1,0076
1,0378
1,0675
1,1707
1,2162
1,2602
1,6712
# of Futures
rounded
3000,0000
2998,9774
3018,5426
2914,7016
2898,8247
2948,4809
3050,2025
3072,3383
3036,3154
3063,3940
3070,9123
3153,7672
3106,6467
3070,4772
3011,4260
2977,8024
3012,6486
2998,8993
3685,2150
3715,5462
3671,2950
3602,0285
3572,4020
3550,1504
3541,0243
3626,6495
3829,0939
3801,8131
3754,4778
3778,3708
134000,0000000000 cleared
uncleared
2950,3782
2439,0244
2439
121.028
118.540
166.279
(86.909)
(125.637)
(4.533)
243.566
297.568
209.725
275.781
294.133
496.265
381.365
293.168
149.159
67.159
152.160
118.634
1.794.569
1.868.645
1.760.819
1.592.167
1.519.995
1.465.807
1.443.629
1.652.548
2.146.581
2.080.161
1.964.824
2.024.162
2.024.162
2.024.182
20,8
100
21
100
21,68
100
22,00
100
22,2
100
2962,705877
2403,8462
2971,023839
2380,9524
3000,0000
2306,0273
3013,807618
2272,7273
3022,603166
2252,2523
89.649
87.196
134.242
(115.322)
(153.494)
(34.137)
210.381
263.603
177.024
242.126
260.213
459.426
346.181
259.254
117.318
36.498
120.269
87.225
1.738.957
1.811.964
1.705.690
1.539.465
1.468.331
1.414.922
1.393.062
1.598.968
2.085.876
2.020.412
1.906.736
1.965.203
1.965.203
1.965.203
68.991
66.560
113.155
(134.050)
(171.860)
(53.640)
188.545
241.260
155.504
219.985
237.898
435.211
323.043
236.943
96.358
16.307
99.277
66.546
1.702.516
1.774.826
1.669.564
1.504.918
1.434.461
1.381.560
1.359.907
1.563.851
2.046.118
1.981.276
1.868.682
1.926.582
1.926.582
1.926.582
(2.358)
42.759
(196.725)
(233.348)
(118.853)
115.700
166.753
83.692
146.140
163.486
354.579
245.937
162.542
26.378
(51.158)
29.190
(2.515)
1.581.867
1.651.899
1.549.945
1.390.469
1.322.226
1.270.985
1.250.010
1.447.533
1.914.613
1.851.807
1.742.752
1.798.798
1.798.798
1.798.798
(31.381)
(33.707)
10.754
(225.300)
(261.396)
(148.555)
82.606
132.919
51.056
112.601
129.694
318.022
210.948
128.756
(5.445)
(81.862)
(2.680)
(33.928)
1.527.525
1.596.543
1.496.060
1.338.882
1.271.622
1.221.120
1.200.446
1.395.114
1.855.444
1.793.544
1.686.062
1.741.283
1.741.283
1.741.283
(50.908)
(53.214)
(9.157)
(243.101)
(278.874)
(167.051)
62.025
111.883
30.757
91.746
108.685
295.313
189.201
107.749
(25.243)
(100.974)
(22.508)
(53.476)
1.493.878
1.562.274
1.462.695
1.306.929
1.240.274
1.190.226
1.169.737
1.362.651
1.818.831
1.757.487
1.650.973
1.705.686
1.705.686
1.705.686
22,5
100
traded
Futures
3035,945735 Price
2222,2222
(79.879)
(82.156)
(38.692)
(269.543)
(304.840)
(194.509)
31.507
80.699
653
60.827
77.538
261.673
156.975
76.607
(54.614)
(129.336)
(51.921)
(82.478)
1.444.197
1.511.679
1.413.426
1.259.733
1.193.965
1.144.583
1.124.365
1.314.705
1.764.798
1.704.270
1.599.174
1.653.144
1.653.144
1.653.144
Cumulative P&L
intraday
16/06/2011
17/06/2011
20/06/2011
06/07/2011
07/07/2011
08/07/2011
11/07/2011
12/07/2011
13/07/2011
14/07/2011
15/07/2011
18/07/2011
19/07/2011
20/07/2011
21/07/2011
22/07/2011
25/07/2011
26/07/2011
24/08/2011
25/08/2011
26/08/2011
29/08/2011
30/08/2011
31/08/2011
01/09/2011
02/09/2011
05/09/2011
06/09/2011
07/09/2011
16/09/2011
interest
rate
20,5
100
comparison of payoffs Futures vs OTC on expiration
Difference OTC
vs listed
www.eurexchange.com
20
-
-
-
-
-
-
27
bough at first trading
bought on 15/07/2011
day and sold (all
and sold (all Futures)
Futures) on 16/08/2011 on 29/08/2011
20,8
24
100
100
Variance Futures on Eurex Exchange
implied vol
(spot to
realized var exp)/
par
from trade settlement variance
date
price
strike II
Accrued
Days
Date
intraday
16/06/2011
17/06/2011
20/06/2011
21/06/2011
22/06/2011
06/07/2011
07/07/2011
08/07/2011
11/07/2011
12/07/2011
13/07/2011
14/07/2011
15/07/2011
18/07/2011
19/07/2011
20/07/2011
21/07/2011
22/07/2011
25/07/2011
26/07/2011
12/08/2011
15/08/2011
16/08/2011
17/08/2011
18/08/2011
19/08/2011
22/08/2011
23/08/2011
24/08/2011
25/08/2011
26/08/2011
29/08/2011
30/08/2011
31/08/2011
01/09/2011
02/09/2011
05/09/2011
06/09/2011
07/09/2011
08/09/2011
09/09/2011
16/09/2011
0
0
1
2
3
4
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
66
0
0
519,789398
340,809657
545,074184
412,6577
382,53721
359,977417
396,249202
501,44077
478,257925
461,485493
445,134157
430,534054
456,859287
456,354515
471,405579
497,260589
479,219926
472,443635
455,68207
1003,0047
982,413989
959,574271
938,352607
1086,23224
1088,60523
1072,1705
1052,84177
1047,01007
1030,98539
1017,7874
1021,79994
1002,52094
1019,81743
1001,39156
1047,04262
1150,24199
1137,72737
1166,63876
1148,54686
1203,85004
1250,1646
trade price
0,21682311
0,21640587
0,22212112
0,21341332
0,20961668
0,19621375
0,19262792
0,2062687
0,22958348
0,23808835
0,22907646
0,239214
0,24350283
0,26611205
0,25332027
0,24093684
0,21726617
0,20675891
0,2213593
0,21882953
0,39625684
0,36182667
0,34235169
0,30647215
0,40643351
0,42323066
0,42359324
0,4068004
0,38390993
0,40937651
0,39608444
0,35586809
0,34832241
0,32101765
0,32692887
0,37222066
0,47486604
0,47524843
0,41575606
0,39965239
0,53286691
0,36197018
470,122601
469,094925
488,75466
459,52618
437,771313
384,476289
368,537501
418,384488
520,480215
542,696237
506,5448
533,718466
541,26284
624,3906
577,117472
540,832881
481,596919
447,869958
482,817499
469,029036
1217,84946
1101,23994
1033,61773
938,652335
1266,2117
1301,52544
1280,0598
1217,03011
1156,95841
1187,3262
1143,0241
1073,68926
1044,03508
1021,76395
1012,63044
1098,32134
1300,88774
1273,59201
1226,2334
1189,33536
1327,76075
1250,1646
interest
rate
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
2,00%
discount factor ARMVM
0,994971589
0,994971589
0,99502611
0,995189689
0,995244221
0,995298757
0,996062567
0,996117147
0,99617173
0,996335498
0,996390093
0,996444691
0,996499292
0,996553897
0,996717727
0,996772343
0,996826963
0,996881585
0,99693621
0,997100103
0,99715474
0,99808403
0,998248112
0,998302812
0,998357515
0,998412221
0,99846693
0,998631075
0,998685796
0,99874052
0,998795247
0,998849977
0,999014185
0,999068927
0,999123672
0,99917842
0,999233171
0,999397442
0,999452205
0,999506971
0,99956174
0,999616512
1
Future price w/ TVA
0,0000
0,0000
0,0000
-0,0002
0,0008
0,0003
-0,0107
-0,0154
-0,0209
-0,0294
-0,0267
-0,0227
-0,0207
-0,0172
-0,0056
0,0028
0,0087
0,0125
0,0132
0,0095
0,0102
0,2769
0,3996
0,4341
0,4649
0,4906
0,5341
0,6706
0,7149
0,7558
0,7934
0,8326
0,9431
0,9762
1,0076
1,0378
1,0675
1,1707
1,2162
1,2602
1,3016
1,3410
1,6712
intraday trade:
bought on 15/07/2011 at 24%
and sold same day at 25%
24
100
2962,705877
2404
3000,0000
2998,9774
3018,5426
2989,4531
2967,8005
2914,7016
2898,8247
2948,4809
3050,2025
3072,3383
3036,3154
3063,3940
3070,9123
3153,7672
3106,6467
3070,4772
3011,4260
2977,8024
3012,6486
2998,8993
3746,0173
3629,6121
3562,1047 Total P&L
3467,2952
3794,3345 sold at V=
3829,5941 traded variance strike
3808,1579 Futures price sold
3745,2110 notional vega sold
3685,2150
3715,5462
3671,2950
3602,0285
3572,4020
3550,1504
3541,0243
3626,6495
3829,0939
3801,8131
3754,4778
3717,5960
3855,9683
3778,3708
total P&L
OTC P&L
discounted OTC P&L
Var amount
final realized
variance strike
realized
implied
remaining days
total days
weighted average implied/ realized
Difference OTC vs listed
www.eurexchange.com
89.649
87.196
134.242
64.323
12.277
(115.322)
(153.494)
(34.137)
210.381
263.603
177.024
242.126
260.213
459.426
346.181
259.254
117.318
36.498
120.269
87.225
1.883.906
1.604.396
1.442.206
34,24%
1034
3562,1047
57.358
1.442.206
1.487.335
1.484.811
2404
1051
433
982
1172
24
66
32,42
42.605
intra day
24% bought at V=
25% sold at
100 Vega K
100
534 traded variance strike
568
3064,0341 Futures Price
3099,6706
intraday quantity
3055,555556
35.162 1st Margin Payment
Margin of selling trade
63.906
end of day
288.336
144.372
530 traded variance strike
563
33.862
3056 # of Futures =100K Vega
2933
(146.570)
3059,4047 Futures Price
3092,6986
P&L end of day
(249.317)
99.069
P&L if the full Futures amount had been sold at 25 vol
(142.884)
101.732
(184.903)
2.098.603
1.743.266
1.537.088
1.247.477
2.246.832
2.354.693
2.289.581
2.097.368
1.914.162
2.006.946
1.871.844
1.679.657 Total P&L
36% Volatility level sold
46.667 notional vega sold
intra day
1077 traded variance strike
3608,3070 Futures price sold
3056 # of Futures =46.667 Vega
1080 traded variance strike
end of day
3608,2967 Futures price sold
1.679.657
1.684.534
1.682.874
2083
1385
576
1429
1296
15
45
37,21
total P&L
OTC P&L
discounted OTC P&L
Var amount
final realized
variance strike
realized
implied
remaining days
total days
weighted average implied/ realized
3.217 Difference OTC vs listed
28
Variance Futures on Eurex Exchange
Different futures prices intraday vs. end of day
bought on 15/07/2011
and sold (all Futures)
on 29/08/2011
24
100
implied vol
(spot to
realized var exp)/
from trade settlement
date
price
Future price w/ TVA
Accrued
Days
Date
intraday
16/06/2011
06/07/2011
07/07/2011
08/07/2011
11/07/2011
12/07/2011
13/07/2011
14/07/2011
15/07/2011
18/07/2011
19/07/2011
20/07/2011
21/07/2011
22/07/2011
25/07/2011
26/07/2011
27/07/2011
intraday trade:
bought on 15/07/2011 at 24%
and sold same day at 25%
24
100
0
0
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
0 trade price
0 0,21682311
382,53721 0,19621375
359,977417 0,19262792
396,249202 0,2062687
501,44077 0,22958348
478,257925 0,23808835
461,485493 0,22907646
445,134157
0,239214
430,534054 0,24350283
456,859287 0,26611205
456,354515 0,25332027
471,405579 0,24093684
497,260589 0,21726617
479,219926 0,20675891
472,443635 0,2213593
455,68207 0,21882953
464,819001 0,23173512
3000,0000
2914,7016
2898,8247
2948,4809
3050,2025
3072,3383
3036,3154
3063,3940
3070,9123
3153,7672
3106,6467
3070,4772
3011,4260
2977,8024
3012,6486
2998,8993
3035,0597
35.162
288.336
144.372
33.862
(146.570)
(249.317)
(142.884)
(184.903)
(74.423)
intra day
24% bought at V=
25% sold at
100 Vega K
100
534 traded variance strike
568
3064,0341 Futures Price
3099,6706
intraday quantity
3055,555556
1st Margin Payment
Margin of selling trade
63.906
end of day
530 traded variance strike
563
3056 # of Futures =100K Vega
2933
3059,4047 Futures Price
3092,6986
99.069
P&L end of day
P&L if the full Futures amount had been sold at 25 vol
101.732
Daily variation margins
www.eurexchange.com
29
Variance Futures on Eurex Exchange
Interest rate interpolation
• Linear interpolation is used in order to determine the risk free interest rate
• Inputs are the EURIBOR rates surrounding the maturity of the Variance Futures:
– TK+1 – maturity of the EURIBOR rate later than the futures maturity
– TK
– maturity of the EURIBOR rate before the futures maturity
– Ti
– maturity of the futures
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30
Variance Futures on Eurex Exchange
Further information
Contact us
Product Development
Eurex Sales
Sascha Semroch
Markus-Alexander Flesch
Eurex Frankfurt AG
Mergenthalerallee 61
65760 Eschborn
Germany
Eurex Zürich AG
Loewenstrasse
8021 Zürich
Switzerland
T: +49 (0)69 211 150 78
T:+41 (0)43 430 7121
[email protected]
[email protected]
www.eurexchange.com
31
Variance Futures on Eurex Exchange
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