Product description & clearing concept
Content Product description Clearing concept Appendix 2
Outline Challenge: Swap products difficult to capture via futures 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 like EURO STOXX 50 Index futures Variance Futures with a standardvariance 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 3
Market snapshot notionalvega volatility strike Bloomberg thomsonreuters VETA <INDEX> CT <0#EVAR:> 4
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 T Variance 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 5
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 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 The discount factor NPVs the expected value of the standard swap between today and maturity = ( ) ARMVM 6
Illustration time to maturity S T F t = = 0 t T 0 t T 0 t T - realized variance standard strike ARMVM realized variance implied volatility 2 - standard strike - 1-D - - ARMVM The cumulative cash flow at final settlement day will be: S T - F t = realized variance implied volatility 2 standard strike - - standard strike + 1-D ARMVM S T final settlement price of the futures F t traded futures price in t 7
Trade Example Trade in an OTC Variance Swap on 15 July 2011 100,000 Vega at 24% volatility 2,083 Variance units 576 Variance strike At settlement on 19 September 2011: Final realized Variance: 1,633 (40.41% volatility) Equity amount: (1,633 576) * 2,083 = 2,201,373 Trade in Variance Futures on 15 July 2011 100,000 Vega at 24% volatility 3,056 Variance Futures at a price of 3,059.4047 The Futures: Total life time : 67 days Accrued days : 22 Remaining life time: 45 days Standard strike : 21.68% At settlement on 19 September 2011: Final settlement price = 3,778.3708 Cumulative variation margins: (3,778.3708-3,059.4047)*3056 = 2,196,840.98 + Cumulative ARMVM (ARMVM T ARMVM t ) * 3056 = 5,159.14 - Discount of the standard swap in t: (1-D t )*(traded variance standard strike) * number of futures = 627.50 Total P&L: = 2,201,373»The difference between implied and realized volatility of 16.41% points results into a 2.2mn profit 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 9
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: into PRELIMINARY Futures prices 2. End of day: 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 10
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 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 11
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 12
Product details Price conversion Standard strike 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 The standard strike will be determined on the first trading day and be equal to the settled implied volatility»1 st settlement price in the futures = 3000 Interest rates 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) Market disruptionevent 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 13
Contract specifications Overview EURO STOXX 50 Variance futures (EVAR) Contract value Contract terms Minimum price change 1 per Variance Futures point 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 0.0001 Variance Futures points Tick value 0.0001 Settlement Final settlement price/ expiration day Final settlement day Last trading day Continuous trading Eurex Trade Entry Services Cash settlement 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 Next trading day following the last trading day One business day before the third Friday of the maturity month 09:00 17:30 CET 18:30 21:00 CET Eurex Trade Entry Services minimum size Trading calendar Trade matching/ Block Trade Entry Service 1 contract 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 Order maintenance Notional vega at volatility Minimum order size = 1 vega Minimum price change = 0.05 volatility points 14
Content Product description Clearing concept Appendix 15
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 automatically cancelled and 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 Cancel/Rebook Block trades can be entered only after the close during the Post Trading Full phase Trade and position adjustments can be done only after the close during the Post Trading Full phase 16
Cancel/Rebook Set up Order book trades will be executed in T7 in vega at volatility strikes and will be converted intraday in futures/-price and quantity Clients will receive trade confirmations from T7 in real time for order book transactions in vol/vega and in futures at PRELIMINARY futures prices The futures will be calculated using previous day s parameters. Only time will be updated, intraday. Time to maturity will be reduced and passed observation days will be increased Clients will receive transaction confirmations from the clearing system for position transactions in real time in futures and PRELIMINARY futures prices Intraday: There will be no live futures price available. It can be calculated using the live volatility quotes and the intraday conversion parameters provided by Eurex Exchange EoD: T7 will calculate the realized variance INCLUDING the EoD closing price of the EURO STOXX 50 Original trades will be cancelled in the clearing system Trade confirmations for the rebooked trades will be sent in vol/vega and in futures with FINAL futures prices Transaction confirmations from the clearing system will be sent in futures with FINAL futures prices EoD Variation Margin will be calculated based on final trade price and EoD settlement price of futures Maturity: The futures settles against the EURO STOXX 50 final settlement price at 12:00 CET on the third Friday of the expiration month. However, no trade/positionadjustments will be allowed until Post-Trading Full phase on the matury day Clearing fees are charged in EUR per futures and also reported accordingly 17
Cancel/Rebook Intraday situation Conversion parameters will be known from the start of day: All parameters as of yesterday s settlement price, except: Time to maturity: -1 day Elapsed days: + 1 day Calculation of margin based on futures and INTERIM futures prices Intraday margin monitoring is done by Eurex Clearing Based on the change in position by the preliminary trade, there can be a real time margin call, if applicable The trades are always booked as open so that preliminary and cancel trades are position-neutral Client s back office receives: A transaction confirmation from the clearing system with futures quantity and INTERIM futures price The confirmation will be marked to indicate the trade to be preliminary The trade adjustment indicator will be set to not adjustable Margin call, if applicable Limitations Block trades can be entered AFTER the final conversion parameters are available (~18:30 CET) Trade/position adjustments can be done after intraday trades are cancelled and re-booked (~18:30 CET) There are no trade/positionadjustments allowed on historical trades either (before ~18:30 CET) 18
Cancel/Rebook End of day situation Conversion parameters are available and the end of day settlement price is calculated Order book trades that took place during the day are converted again into futures and traded futures prices based on end of day parameters Original trades (FreeText1 = PRELIMINARY) are AUTOMATICALLY cancelled The cancel message will contain the Eurex Original Order ID (containing the T7 Order ID) New transaction confirmations are AUTOMATICALLY sent based on the FINAL futures prices The new trade will be marked as final trade (FreeText1 = FINAL_) The new trade will contain the Eurex Original Order ID (containing the T7 Order ID) The transactions can be linked in the Eurex Clearing GUI by the Eurex Original Order ID With the beginning of the Post Trading Full phase the following is allowed: Block trades can be entered Trade/position adjustments can be done Variation Margin is calculated based on the futures A separate trade report contains for all transactions: (original) vega, vol strikes, futures quantities and final traded futures prices 19
Summary: Trade processing in the Eurex Clearing system Preliminarytrade Cancelledtrade Final trade Timing - Intraday - End of day - End of day Quantity/ price - futures quantity - INTERIM futures price - Original trade is AUTOMATICALLY cancelled - No changes to the quantity - FINAL futures price resulting from the end of day conversion Required flag/id - Eurex Original Order ID (containing the T7 Order ID) - FreeText1 marked as preliminary trade = PRELIMINARY - Time stamp of the original trade - The trade is NOT ADJUSTABLE (via Trade adjustment indicator in Eurex System) - Eurex Original Order ID (containing the T7 Order ID) - FreeText1 marked as cancelled trade = CANCEL - Time stamp of the cancelled trade - Eurex Original Order ID (containing the NTA Order ID) - FreeText1 marked as final trade = FINAL_ - Time stamp of the final trade - The new trade 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 trade will be marked to indicate it is preliminary - The cancel message will indicate the trade to be cancelled - Transaction confirmations from the clearing system will be sent again in futures with FINAL futures prices 20
Trade Capture Report (TCR): Attributes TradeReport Type Secondary Order ID Preliminary trade Cancelled trade Final trade 1 6 0 000000000012 000000000012 000000000012 Comment 0 = Submit (New trade; no changes) 1 = Alleged (Preliminary; NEW) 6 = Trade Report Cancel; no changes) T7 Order ID The transactions can be linked on the Eurex Clearing GUI using this Original Order ID Trade Report ID 00008700000C 00009900000C 00010600000C EurexTranID + Suffix (here always 00000)+ historical adjustmentindicator (here always C ) FreeText1 PRELIM000087 CANCEL000087 FINAL_000087 There will be new constant CANCEL to distuinguish between reversal of the preliminary trade from the bust of final trade; FINAL_ will link the final trade to the preliminary trade 87 stands for Eurex Transaction ID in this example Position Effect 1) O 2) O C C C O All preliminary trades will be booked to open at Eurex Clearing; Example 1): Original trade executed to close Example 2): Original trade executed to open 21
June 2013 An example Buy 100.000 vega at 24 vol strike T7 Clearing System Eurex Clearing intraday Real time trade confirmation: 100.000 vega at 24 vol Strike 3056 futures at 3064,0341 intraday Real time transaction confirmation: 3056 futures at 3064,0341 FreeText1 = PRELIMINARY Trade Adjustment Indicator: not adjustable End of day, the final conversion parameters are calculated Trade confirmation: 100.000 vega at 24 vol strike 3056 futures at 3059,4047 Transaction cancellation: 3056 futures at 3064,0341 FreeText1 = CANCEL Transaction confirmation: 3056 futures at 3059,4047 FreeText1 = FINAL_ 22
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 23
Time axis 18:30 CET Pre trading Trading TCA Post Trading Full Post late 1 Post late 2 Post restricted Pre-Trading Enter quotes and orders Trading Only order book trades are accepted No support of trade adjustments Technical closing auction (auction without trading) Availability of conversion parameters Addition of EURO STOXX 50 close price to the realized variance Calculation of final conversion parameters Cancellations Re-bookings Post-Trading Full Enter quotes and order for following day Availability of post trade functions Enter Block Trades 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 24
Content Product description Clearing concept Appendix 25
Appendix 26
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 (σ 2 realized) = 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 27
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 ( ) ( ( )) Note there will be no trade/position adjustments possible until Post-Trading Full phase =0 28
Rounded to the nearest integer Trades at different prices on 1st trading day Date vol strike 20,5 20,8 21 21,68 22,00 22,2 22,5 vega '000 100 100 100 100 100 100 100 implied vol (spot to realized var exp)/ par traded Accrued from trade settlement variance interest Futures Days date price strike II rate discount factor ARMVM Future price w/ TVA 2950,3782 2962,705877 2971,023839 3000,0000 3013,807618 3022,603166 3035,945735 Price # of Futures 2439,0244 2403,8462 2380,9524 2306,0273 2272,7273 2252,2523 2222,2222 intraday 0 0trade price 2,00% 0,994971589 0,0000 rounded 2439 16/06/2011 0 0 0,21682311 470,122601 2,00% 0,994971589 0,0000 3000,0000 121.028 89.649 68.991 - (31.381) (50.908) (79.879) 17/06/2011 1 519,789398 0,21640587 469,094925 2,00% 0,99502611 0,0000 2998,9774 118.540 87.196 66.560 (2.358) (33.707) (53.214) (82.156) 20/06/2011 2 340,809657 0,22212112 488,75466 2,00% 0,995189689-0,0002 3018,5426 166.279 134.242 113.155 42.759 10.754 (9.157) (38.692) 06/07/2011 14 382,53721 0,19621375 384,476289 2,00% 0,996062567-0,0107 2914,7016 (86.909) (115.322) (134.050) (196.725) (225.300) (243.101) (269.543) 07/07/2011 15 359,977417 0,19262792 368,537501 2,00% 0,996117147-0,0154 2898,8247 (125.637) (153.494) (171.860) (233.348) (261.396) (278.874) (304.840) 08/07/2011 16 396,249202 0,2062687 418,384488 2,00% 0,99617173-0,0209 2948,4809 (4.533) (34.137) (53.640) (118.853) (148.555) (167.051) (194.509) 11/07/2011 17 501,44077 0,22958348 520,480215 2,00% 0,996335498-0,0294 3050,2025 243.566 210.381 188.545 115.700 82.606 62.025 31.507 12/07/2011 18 478,257925 0,23808835 542,696237 2,00% 0,996390093-0,0267 3072,3383 297.568 263.603 241.260 166.753 132.919 111.883 80.699 13/07/2011 19 461,485493 0,22907646 506,5448 2,00% 0,996444691-0,0227 3036,3154 209.725 177.024 155.504 83.692 51.056 30.757 653 14/07/2011 20 445,134157 0,239214 533,718466 2,00% 0,996499292-0,0207 3063,3940 275.781 242.126 219.985 146.140 112.601 91.746 60.827 15/07/2011 21 430,534054 0,24350283 541,26284 2,00% 0,996553897-0,0172 3070,9123 294.133 260.213 237.898 163.486 129.694 108.685 77.538 18/07/2011 22 456,859287 0,26611205 624,3906 2,00% 0,996717727-0,0056 3153,7672 496.265 459.426 435.211 354.579 318.022 295.313 261.673 19/07/2011 23 456,354515 0,25332027 577,117472 2,00% 0,996772343 0,0028 3106,6467 381.365 346.181 323.043 245.937 210.948 189.201 156.975 20/07/2011 24 471,405579 0,24093684 540,832881 2,00% 0,996826963 0,0087 3070,4772 293.168 259.254 236.943 162.542 128.756 107.749 76.607 21/07/2011 25 497,260589 0,21726617 481,596919 2,00% 0,996881585 0,0125 3011,4260 149.159 117.318 96.358 26.378 (5.445) (25.243) (54.614) 22/07/2011 26 479,219926 0,20675891 447,869958 2,00% 0,99693621 0,0132 2977,8024 67.159 36.498 16.307 (51.158) (81.862) (100.974) (129.336) 25/07/2011 27 472,443635 0,2213593 482,817499 2,00% 0,997100103 0,0095 3012,6486 152.160 120.269 99.277 29.190 (2.680) (22.508) (51.921) 26/07/2011 28 455,68207 0,21882953 469,029036 2,00% 0,99715474 0,0102 2998,8993 118.634 87.225 66.546 (2.515) (33.928) (53.476) (82.478) 24/08/2011 49 1047,01007 0,38390993 1156,95841 2,00% 0,99874052 0,7558 3685,2150 1.794.569 1.738.957 1.702.516 1.581.867 1.527.525 1.493.878 1.444.197 25/08/2011 50 1030,98539 0,40937651 1187,3262 2,00% 0,998795247 0,7934 3715,5462 1.868.645 1.811.964 1.774.826 1.651.899 1.596.543 1.562.274 1.511.679 26/08/2011 51 1017,7874 0,39608444 1143,0241 2,00% 0,998849977 0,8326 3671,2950 1.760.819 1.705.690 1.669.564 1.549.945 1.496.060 1.462.695 1.413.426 29/08/2011 52 1021,79994 0,35586809 1073,68926 2,00% 0,999014185 0,9431 3602,0285 1.592.167 1.539.465 1.504.918 1.390.469 1.338.882 1.306.929 1.259.733 30/08/2011 53 1002,52094 0,34832241 1044,03508 2,00% 0,999068927 0,9762 3572,4020 1.519.995 1.468.331 1.434.461 1.322.226 1.271.622 1.240.274 1.193.965 31/08/2011 54 1019,81743 0,32101765 1021,76395 2,00% 0,999123672 1,0076 3550,1504 1.465.807 1.414.922 1.381.560 1.270.985 1.221.120 1.190.226 1.144.583 01/09/2011 55 1001,39156 0,32692887 1012,63044 2,00% 0,99917842 1,0378 3541,0243 1.443.629 1.393.062 1.359.907 1.250.010 1.200.446 1.169.737 1.124.365 02/09/2011 56 1047,04262 0,37222066 1098,32134 2,00% 0,999233171 1,0675 3626,6495 1.652.548 1.598.968 1.563.851 1.447.533 1.395.114 1.362.651 1.314.705 05/09/2011 57 1150,24199 0,47486604 1300,88774 2,00% 0,999397442 1,1707 3829,0939 2.146.581 2.085.876 2.046.118 1.914.613 1.855.444 1.818.831 1.764.798 06/09/2011 58 1137,72737 0,47524843 1273,59201 2,00% 0,999452205 1,2162 3801,8131 2.080.161 2.020.412 1.981.276 1.851.807 1.793.544 1.757.487 1.704.270 07/09/2011 59 1166,63876 0,41575606 1226,2334 2,00% 0,999506971 1,2602 3754,4778 1.964.824 1.906.736 1.868.682 1.742.752 1.686.062 1.650.973 1.599.174 16/09/2011 66 1250,1646 0,36197018 1250,1646 2,00% 1 1,6712 3778,3708 2.024.162 1.965.203 1.926.582 1.798.798 1.741.283 1.705.686 1.653.144 67 35,3576668 134000,0000000000 cleared 2.024.162 1.965.203 1.926.582 1.798.798 1.741.283 1.705.686 1.653.144 uncleared 2.024.182 1.965.203 1.926.582 1.798.798 1.741.283 1.705.686 1.653.144 comparison of payoffs Futures vs OTC on expiration Cumulative P&L Difference OTC vs listed 20 - - - - - - 29
Date Accrued Days realized var from trade date implied vol (spot to exp)/ settlement price par variance strike II bough at first trading day and sold (all Futures) on 16/08/2011 interest rate discount factor ARMVM Future price w/ TVA 2962,705877 2404 bought on 15/07/2011 and sold (all Futures) on 29/08/2011 20,8 24 24 100 100 100 intraday 0 0trade price 2,00% 0,994971589 0,0000 16/06/2011 0 0 0,21682311 470,122601 2,00% 0,994971589 0,0000 3000,0000 89.649 17/06/2011 1 519,789398 0,21640587 469,094925 2,00% 0,99502611 0,0000 2998,9774 87.196 20/06/2011 2 340,809657 0,22212112 488,75466 2,00% 0,995189689-0,0002 3018,5426 134.242 21/06/2011 3 545,074184 0,21341332 459,52618 2,00% 0,995244221 0,0008 2989,4531 64.323 22/06/2011 4 412,6577 0,20961668 437,771313 2,00% 0,995298757 0,0003 2967,8005 12.277 06/07/2011 14 382,53721 0,19621375 384,476289 2,00% 0,996062567-0,0107 2914,7016 (115.322) 07/07/2011 15 359,977417 0,19262792 368,537501 2,00% 0,996117147-0,0154 2898,8247 (153.494) intra day 08/07/2011 16 396,249202 0,2062687 418,384488 2,00% 0,99617173-0,0209 2948,4809 (34.137) 24% bought at V= 25% sold at 11/07/2011 17 501,44077 0,22958348 520,480215 2,00% 0,996335498-0,0294 3050,2025 210.381 100 Vega K 100 12/07/2011 18 478,257925 0,23808835 542,696237 2,00% 0,996390093-0,0267 3072,3383 263.603 534 traded variance strike 568 13/07/2011 19 461,485493 0,22907646 506,5448 2,00% 0,996444691-0,0227 3036,3154 177.024 3064,0341 Futures Price 3099,6706 14/07/2011 20 445,134157 0,239214 533,718466 2,00% 0,996499292-0,0207 3063,3940 242.126 intraday quantity 3055,555556 15/07/2011 21 430,534054 0,24350283 541,26284 2,00% 0,996553897-0,0172 3070,9123 260.213 35.162 1st Margin Payment Margin of selling trade 63.906 18/07/2011 22 456,859287 0,26611205 624,3906 2,00% 0,996717727-0,0056 3153,7672 459.426 288.336 end of day 19/07/2011 23 456,354515 0,25332027 577,117472 2,00% 0,996772343 0,0028 3106,6467 346.181 144.372 530 traded variance strike 563 20/07/2011 24 471,405579 0,24093684 540,832881 2,00% 0,996826963 0,0087 3070,4772 259.254 33.862 3056 # of Futures =100K Vega 2933 21/07/2011 25 497,260589 0,21726617 481,596919 2,00% 0,996881585 0,0125 3011,4260 117.318 (146.570) 3059,4047 Futures Price 3092,6986 22/07/2011 26 479,219926 0,20675891 447,869958 2,00% 0,99693621 0,0132 2977,8024 36.498 (249.317) P&L end of day 99.069 25/07/2011 27 472,443635 0,2213593 482,817499 2,00% 0,997100103 0,0095 3012,6486 120.269 (142.884) P&L if the full Futures amount had been sold at 25 vol 101.732 26/07/2011 28 455,68207 0,21882953 469,029036 2,00% 0,99715474 0,0102 2998,8993 87.225 (184.903) 12/08/2011 41 1003,0047 0,39625684 1217,84946 2,00% 0,99808403 0,2769 3746,0173 1.883.906 2.098.603 15/08/2011 42 982,413989 0,36182667 1101,23994 2,00% 0,998248112 0,3996 3629,6121 1.604.396 1.743.266 16/08/2011 43 959,574271 0,34235169 1033,61773 2,00% 0,998302812 0,4341 3562,1047 Total P&L 1.442.206 1.537.088 17/08/2011 44 938,352607 0,30647215 938,652335 2,00% 0,998357515 0,4649 3467,2952 1.247.477 18/08/2011 45 1086,23224 0,40643351 1266,2117 2,00% 0,998412221 0,4906 3794,3345 sold at V= 34,24% 2.246.832 19/08/2011 46 1088,60523 0,42323066 1301,52544 2,00% 0,99846693 0,5341 3829,5941 traded variance strike 1034 2.354.693 22/08/2011 47 1072,1705 0,42359324 1280,0598 2,00% 0,998631075 0,6706 3808,1579 Futures price sold 3562,1047 2.289.581 23/08/2011 48 1052,84177 0,4068004 1217,03011 2,00% 0,998685796 0,7149 3745,2110 notional vega sold 57.358 2.097.368 24/08/2011 49 1047,01007 0,38390993 1156,95841 2,00% 0,99874052 0,7558 3685,2150 1.914.162 25/08/2011 50 1030,98539 0,40937651 1187,3262 2,00% 0,998795247 0,7934 3715,5462 2.006.946 26/08/2011 51 1017,7874 0,39608444 1143,0241 2,00% 0,998849977 0,8326 3671,2950 1.871.844 29/08/2011 52 1021,79994 0,35586809 1073,68926 2,00% 0,999014185 0,9431 3602,0285 1.679.657 Total P&L 30/08/2011 53 1002,52094 0,34832241 1044,03508 2,00% 0,999068927 0,9762 3572,4020 36% Volatility level sold 31/08/2011 54 1019,81743 0,32101765 1021,76395 2,00% 0,999123672 1,0076 3550,1504 intra day 46.667 notional vega sold 01/09/2011 55 1001,39156 0,32692887 1012,63044 2,00% 0,99917842 1,0378 3541,0243 1077 traded variance strike 02/09/2011 56 1047,04262 0,37222066 1098,32134 2,00% 0,999233171 1,0675 3626,6495 3608,3070 Futures price sold 05/09/2011 57 1150,24199 0,47486604 1300,88774 2,00% 0,999397442 1,1707 3829,0939 3056 # of Futures =46.667 Vega 06/09/2011 58 1137,72737 0,47524843 1273,59201 2,00% 0,999452205 1,2162 3801,8131 1080 traded variance strike 07/09/2011 59 1166,63876 0,41575606 1226,2334 2,00% 0,999506971 1,2602 3754,4778 end of day 3608,2967 Futures price sold 08/09/2011 60 1148,54686 0,39965239 1189,33536 2,00% 0,99956174 1,3016 3717,5960 09/09/2011 61 1203,85004 0,53286691 1327,76075 2,00% 0,999616512 1,3410 3855,9683 16/09/2011 66 1250,1646 0,36197018 1250,1646 2,00% 1 1,6712 3778,3708 total P&L 1.442.206 1.679.657 total P&L OTC P&L 1.487.335 1.684.534 OTC P&L discounted OTC P&L 1.484.811 1.682.874 discounted OTC P&L Var amount 2404 2083 Var amount final realized 1051 1385 final realized variance strike 433 576 variance strike realized 982 1429 realized implied 1172 1296 implied remaining days 24 15 remaining days total days 66 45 total days weighted average implied/ realized 32,42 37,21 weighted average implied/ realized Difference OTC vs listed 42.605 3.217 Difference OTC vs listed intraday trade: bought on 15/07/2011 at 24% and sold same day at 25% 30
Different futures prices intraday vs. end of day Date Accrued Days realized var from trade date implied vol (spot to exp)/ settlement price Future price w/ TVA bought on 15/07/2011 and sold (all Futures) on 29/08/2011 intraday trade: bought on 15/07/2011 at 24% and sold same day at 25% 24 24 100 100 intraday 0 0trade price 16/06/2011 0 0 0,21682311 3000,0000 06/07/2011 14 382,53721 0,19621375 2914,7016 07/07/2011 15 359,977417 0,19262792 2898,8247 intra day 08/07/2011 16 396,249202 0,2062687 2948,4809 24% bought at V= 25% sold at 11/07/2011 17 501,44077 0,22958348 3050,2025 100 Vega K 100 12/07/2011 18 478,257925 0,23808835 3072,3383 534 traded variance strike 568 13/07/2011 19 461,485493 0,22907646 3036,3154 3064,0341 Futures Price 3099,6706 14/07/2011 20 445,134157 0,239214 3063,3940 intraday quantity 3055,555556 15/07/2011 21 430,534054 0,24350283 3070,9123 35.162 1st Margin Payment Margin of selling trade 63.906 18/07/2011 22 456,859287 0,26611205 3153,7672 288.336 end of day 19/07/2011 23 456,354515 0,25332027 3106,6467 144.372 530 traded variance strike 563 20/07/2011 24 471,405579 0,24093684 3070,4772 33.862 3056 # of Futures =100K Vega 2933 21/07/2011 25 497,260589 0,21726617 3011,4260 (146.570) 3059,4047 Futures Price 3092,6986 22/07/2011 26 479,219926 0,20675891 2977,8024 (249.317) P&L end of day 99.069 25/07/2011 27 472,443635 0,2213593 3012,6486 (142.884) P&L if the full Futures amount had been sold at 25 vol 101.732 26/07/2011 28 455,68207 0,21882953 2998,8993 (184.903) 27/07/2011 29 464,819001 0,23173512 3035,0597 (74.423) Daily variation margins 31
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: T K+1 maturity of the EURIBOR rate later than the futures maturity T K maturity of the EURIBOR rate before the futures maturity T i maturity of the futures 32
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