Variance Futures

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					Variance Futures


Variance Futures on Bclear
from 15 December 2006
Version 1.4
14 December 2006
Contents
 Variance Futures
 Variance Futures on Bclear
 Variance Swaps vs. Variance Futures
 Why use Variance Futures?
 Advantages versus OTC
 How they are traded
 Fair Value
 Examples
 Settlement and Margining
 Fees
 Trade entry
 Contacts
 Appendices




                             2
Variance Futures

 OTC market has seen substantial growth in variance
 swap activity over recent years

 Increased demand for tools which provide exposure
 purely to volatility

 Variance futures are a „listed‟ version of an OTC variance
 swap

 Euronext.liffe will offer the first cleared-only, on-exchange
 solution for variance futures



                            3
Variance Futures on Bclear
 Variance futures on FTSE 100, CAC 40 and AEX Indices were launched on
 Friday 15 September 2006 on Bclear only. No products on LIFFE
 CONNECT®

 1, 2, 3, 6, 9, 12 and 15 month contracts are available on the FTSE100, the
 CAC 40 and the AEX

 Contracts are fixed term „end to end‟. Different contract codes for 1, 2, 3, 6, 9,
 12 and 15 month contracts

 Contract valued at £50 per variance point for variance futures on the FTSE
 100 (e.g. value £10,000 at 200) and €50 per variance point for variance
 futures on AEX and CAC 40 (e.g. value €12,000 at 240)

 Last Trading Day is the standard Third Friday expiry

 Cleared by LCH.Clearnet Ltd




                                     4
 Variance Swaps vs. Variance Futures
 Variance Swaps                                                             Variance Futures
     - Flexible start dates                                                    - Fixed start dates
     - Typically quarterly expiries                                            - At trade initiation value of contract is 100%
                                                                                 implied variance only if traded on the listing day
     - At trade initiation value of contract is 100%                             of contract or the following day
       implied variance regardless of trade date
                                                                               - If trade initiated on business day other than the
                                                                                 listing day of contract or the following business
                                                                                 day, then the value of contract is made up of
                                                                                 implied and accrued realized variance

                                                                               - Payout = no. of lots x variance point value x
                                                                                 (realized variance – implied variance), reflecting
     - Payout = €/£notional variance x ((realized vol)2 -                        payoff of variance swap (see Appendix 3)
       (implied vol)2 )
                                                                               - Standardised contract specifications
     - Non-standardised contracts                                              - First cleared, on-exchange solution with central
                                                                                 counterparty
     - Large OTC variance swap market with
       counterparty credit risk                                                - Disruption days governed by Exchange rules
                                                                                 (based on ISDA® rules)
     - Disruption days governed by ISDA® rules
ISDA® is a registered trademark of the International Swaps and Derivatives Association, Inc.




                                                                      5
Variance Futures - Why use Variance Futures?

 Exposure to pure volatility

 Hedge volatility exposure of stock portfolios (secondary solution to buying puts given
 that puts offer more leverage and have a known loss)

 Require no delta hedging

 Easy to hedge using strips of options

 Trade views on changes in implied volatility or fluctuations in the term structure

 Cross index volatility trades (i.e. equity volatility on one index is high or low relative to
 another)

 Cross country volatility trades (i.e. equity volatility in one country is high or low relative
 to another)




                                           6
Variance Futures on Bclear – Advantages
vs. OTC
 Bclear provides unique „cleared, on-exchange‟ solution for variance futures

 Matches OTC advantage of non publication of trades

 Close out of open position with different counterparty

 More users able to access the market as some users unable to trade OTC

 Central counterparty, same contract netting and guarantee (LCH.Clearnet Ltd)

 Reduced operational risk e.g. instant trade confirmation

 Frees up credit lines

 Daily independent mark-to-market and variation margin

 Initial margin reduces as contract approaches maturity




                                        7
Variance Futures – How they are traded

 Similar to variance swaps

 Difference:
  - If a trade is initiated on a business day other than the listing day or the
    business day following the listing day of the futures contract, then the
    value of the futures contract will be made up of implied and accrued
    realized variance (contract has accrued realized variance from the
    business day following the listing day to the trade day), therefore the
    futures variance price and number of lots traded must account for the
    realized variance in the futures contract at the trade date

  - If the intended trading implied variance level is higher than the realized
    variance in the futures contract, then the trader must trade more
    contracts at a lower total variance level. If the intended trading implied
    variance level is lower than the realized variance in the futures contract,
    then the trader must trade fewer contracts at a higher total variance level



                                     8
Variance Futures – Fair Value
Value of Variance Future during life of contract




     Futures first listing date                     At maturity
          100% Implied                             100% Realized




                                      9
Variance Futures – Example 1
Trader buys a 12 month FTSE 100 variance future with an exposure of approx. £100,000 per volatility point

          - implied volatility (“imp vol”) = 14

The per volatility point amount (£101,000 rounded) is equivalent to 72 contracts (contract valued at £50 per variance
point)1

Scenario 1
Realized volatility (“re vol”) = 18
Difference in volatility = 4 volatility points
Payout in swap terminology = £notional x ((re vol)2 - (imp vol)2 )
Payout of futures = no. of lots x variance point value x (realized variance – implied variance)
                     = (72 x £50) x (324 - 196) = £460,800 (profit)

Scenario 2
Realized volatility = 10
Difference in volatility = minus 4 volatility points
Payout in swap terminology = £notional x ((re vol)2 - (imp vol)2 )
Payout of futures = no. of lots x variance point value x (realized variance – implied variance)
                       = (72 x £50) x (100 - 196) = £345,600 (loss)

Note: Variance futures have a non-linear payoff i.e. larger payoff to the long futures position when realized variance exceeds implied variance,
compared to the loses incurred when implied variance exceeds realized variance by the same volatility point magnitude

Note: these calculations are approximations only and are simplifications of the actual calculations involved in trading variance futures. Appendix
3 outline the formulas to be used by Bclear in the above calculations

1 See   Appendix 3 for the formula to convert a per volatility point amount into number of futures contracts




                                                                     10
Variance Futures – Example 2
  Trader buys a 12 month FTSE 100 variance future with an exposure of approx. £100,000
  per volatility point. The contract already has 25 days realized variance at 169 (13 vol)

 To replicate a variance swap trade the trader will need to adjust the trade price and the
 number of contracts traded to take into account the realized variance accrued in the
 contract at the trade date

  Step 1 - Adjustment to the trade price

 The remaining implied variance traded at 196 (implied volatility at 14)
 Traded level = (re vol)2 x proportion of time elapsed + (imp vol)2 x proportion of time
 remaining
          = (169 x (25/252)+ 196 x (227/252)) = 193.5 (rounded from 193.3)

  Step 2 - Adjustment to the number of futures contracts traded

 The per volatility point amount (£100,000) is approximated to 80 contracts (contract
 valued at £50 per variance point)1
1 See   Appendix 3 for the formula to convert a per volatility point amount into number of futures contracts




                                                                       11
Variance Futures – Example 2
 Scenario 1

 Realized variance for the whole life of the contract (EDSP) = (realized variance at trade date x elapsed proportion of
 time of the contract‟s life) + (realized variance from the trade date to the maturity date x proportion of time of the
 contract‟s life)

           = (169 x (25/252) + 324 x (227/252) = 308.5 (realized volatility for the contract‟s whole life is 17.564)

 Realized variance from the trade date until maturity = 324 (realized volatility from the trade date until maturity is 18)
 Difference in volatility = realised volatility from trade date until maturity (18) – implied volatility (14) = 4 volatility points
 Payout of futures = no. of lots x variance point value x (realized variance – implied variance)

           = (80 x £50) x (308.5 – 193.5) = £460,000 (profit)

 Scenario 2

 Realized variance for whole life of the contract (EDSP) = (169 x (25/252)) + (100 x (227/252) = 107 (rounded from
 106.9) (realized volatility for the contract‟s whole life is 10.339)

 Realized variance from the trade date until maturity = 100 (realized volatility from the trade date until maturity is 10)
 Difference in volatility = realised volatility from trade date until maturity (10) – implied volatility (14) = minus 4 volatility
 points

           = (80 x £50) x (107 – 193.5) = £346,000 (loss)

 Please note that these calculations are approximations only and are simplifications of the actual calculations involved in trading variance
 futures. Appendix 3 outlines the formulas to be used by Bclear in the above calculations




                                                               12
Variance Futures on Bclear – Settlement
and Margining
 Daily Settlement
  - marked to market daily based on fair value calculation
  - fair value calculation will combine realized variance in the contract period
    up to that date and a theoretical calculation of the implied variance of the
    remaining life of the contract derived from index options prices in the
    central order book

 Margining
  - based on the daily settlement price in variance points
  - reduced by a coefficient determined by the time remaining to expiry
  - different expiries will have different margin levels applied due to different
    times to expiry and settlement prices (see Appendix 2)

 Exchange Delivery Settlement Price (“EDSP”)
  - realized variance over the life of the contract




                                    13
Fees

Exchange transaction fees and LCH.Clearnet Ltd clearing and cash settlement
fees are as follows
 FTSE 100 Variance Futures Contracts

                                                                                                 Fee Cap
                     Fee per lot                              Proprietary Business                Client Business
                Exchange    Clearing           Cash     Exchange    Clearing     Cash     Exchange    Clearing     Cash
                   fee         fee           Settlement    fee         fee     Settlement    fee         fee    Settlement
 FTSE 100                                        fee                               fee                              fee
 Variance         £6.75          £0.75         £0.25     £1,500       £375      £1,875     £3,000       £750      £3,750



 AEX and CAC40 Variance Futures Contracts

                                                                                                 Fee Cap
                     Fee per lot                              Proprietary Business               Client Business
                Exchange    Clearing           Cash     Exchange    Clearing     Cash     Exchange   Clearing    Cash
  AEX and          fee         fee           Settlement    fee         fee     Settlement    fee        fee    Settlement
   CAC40                                         fee                               fee                             fee
  Variance        € 6.75         € 1.25        € 0.35        € 1,600         € 400         € 2,000       € 3,200         € 800    € 4,000


Cash Settlement fee caps are applied to the total expiring volume at TRS account level (i.e. House, non-Segregated, Segregated)




                                                                     14
Variance Futures – Trade entry
 Users enter the following information on the Bclear trade submission screen:

        - volume (number of futures contracts; minimum one contract)
        - total variance trade price (combined realized and implied variance in the contract)
        - expiry date

 Bclear will automatically calculate:

        -   approximation of the local vega exposure in the currency of the contract
        -   implied variance
        -   realized variance*
        -   business days remaining in the contract‟s life

By automating the above calculations, users will need to make fewer additional
calculations to cater for the fixed end-to-end term structure of variance futures
contracts

*The calculation used for calculating realized variance for contracts initiated on a business day other than the first trading
day of the contract is the same calculation as that used when closing out a variance swap position in the OTC market
prior to the expiry date




                                                          15
      Variance Futures – Trade entry




      User enters number         User enters expiry date here. Variance futures               User enters total
      of futures contracts       expire on 3rd Friday of quarterly expiry month                variance here

Local Vega Approximation, Remaining Days, Realized Variance, Implicit (Implied) Variance are automatically calculated by Bclear




                                                              16
Contacts

 Questions on Variance Futures:
  - Equity Product Development +44 (0)20 7379 2200

 How to access Bclear:
  - Membership Operations +44 (0)20 7379 2897


 Customer test environment available in Bclear test
 environment; contact
  - Customer Test Support Group (CTSG) – 020 7379 2983 or email
    bcleartest@liffe.com
  - Your Account Manager




                            17
Appendices

 Appendix 1 – Contract Specifications
 Appendix 2 – Margin rates
 Appendix 3 – Formulas
 Appendix 4 – Expiry cycles




                         18
Appendix 1 – Contract specifications
Underlying                               FTSE 100, CAC 40 or AEX indices
Unit of trading                          FTSE 100 - Contract Valued at £50 per variance point (e.g. value £10,000 at 200.0),
                                         AEX and CAC 40 - Contract Valued at €50 per variance point (e.g. value €12,000 at 240.0)

Contract Period                          1, 2, 3, 6, 9, 12 and 15 months
Contract Cycle                           March, June, September, December
Quotation                                Variance points, e.g. 360.5
Minimum price movement                   0.1
(tick size and value)                    FTSE 100 - £5
                                         AEX and CAC 40 - €5
Last trading day                         Third Friday of the appropriate month. In the event of the third Friday not being a business day, the
                                         Last Trading Day shall normally be the last business day preceding the third Friday
                                         FTSE 100
                                         10:10 London time
                                         CAC 40 and AEX
                                         15:00 London time


EDSP                                     Realized variance over the life of the contract, rounded to the nearest 0.1 variance point*
Clearing                                 TRS/CPS (Financials TRS) LCH.Clearnet Ltd
Delivery day (cash settlement)           First business day after the Last Trading Day
Trading hours                            FTSE 100, CAC 40 and AEX
                                         08:00-17:00 London time
Disruption Days                          Disruption days governed by Exchange rules (based on ISDA rules)


*In the case of an expiring variance future, the variance for that day will be measured using the EDSP of the relevant stock index future and option
contract




                                                                          19
Appendix 2 – Margin rates
 Margin levels
  - The margin „band‟ applied is determined by the daily settlement price of the contract and varied
     according to time remaining to expiry

                           Fraction of time prior to Maturity
                                   Maturity          Discount
                           100%      to      90%        0%
                           <90%      to      40%       10%
                           <40%      to      20%       20%
                           <20%      to      10%       30%
                           <10%      to       0%       50%



  -   A full list of contract tables for FTSE 100, CAC 40 and AEX can be found at
      http://www.lch.com/Images/LIFFE_LCP_174_tcm3-29636.xls, below is an example for the 1
      month FTSE Variance Future London Span Parameter.




                                            20
Appendix 2 – Margin rates

              Daily Settlement Volatility Equivalent Structure Variance Structure              Margin
              Scenarios         From                 To          From              To
                              1                    0          13                 0    168.99      3,300
                              2                   13          16               169    255.99      5,000
                              3                   16          20               256    399.99      7,800
                              4                   20          25               400    624.99     12,200
    1 month




                              5                   25          30               625    899.99     17,600
                              6                   30          35               900 1224.99       23,900
                              7                   35          40             1225 1599.99        31,200
                              8                   40          47             1600 2208.99        43,100
                              9                   47          55             2209 3024.99        59,000
                             10                   55          70             3025 4899.99        95,600
                             11                   70          85             4900 7224.99       140,900
                             12                   85         100             7225 10000.00      195,000
                             13                    >         100                 > 10000.00     195,000




                                                   21
Appendix 3 - Formulas

         Exchange Delivery Settlement Price (“EDSP”)
         - EDSP will be realized variance only
                                                                                        2
                                                           p t 
                                                         Na
                                                      Ln 
                                                            p 
                                                                  
                                   EDSP      252 
                                                    t 1
                                                           t 1 
                                                                                           10 ,000
Where:                                                                 Ne

     Na is the actual number of Observation Days in the contract's life (normally from the business day following the futures contract's listing day up to and
     including the Expiry Day, excluding Disrupted Days)
     Ne is the expected number of Business Days in the contract‟s life (normally from the business day following the futures contract‟s listing day up to and
     including the Expiry Day, including Disrupted Days). This is fixed from the listing day
     Ln is the natural logarithm
     pt is the closing index level on the Observation Day and where t=1, is the closing index level on the first business day following the listing day of the futures
     contract. In the case of an expiring variance future, the variance for that day will be measured using the EDSP of the relevant index options contract
     (subject to Disruption Day rules)
     pt-1 is the closing index level of the previous Observation Day and where t=1, p t-1 is the closing index level on the Observation Start Date (normally the
     closing index level on the first day of contract listing)
     t is the relevant Observation Day




                                                                           22
 Appendix 3 - Formulas
         Daily Settlement Price (“DSP”)

  DSP will be sum of:
     - realized variance – derived from index movements over the life of the contract to date
     - implied variance – synthesised from settlement prices of the associated LIFFE CONNECT® central order book index options



                                  (RV  n)  ( IV  ( Na  n))
Where:
                              
                                              Ne
         Na is the actual number of Observation Days in the contract's life (normally from the business day following the futures contract's listing day up to and including the Expiry
         Day, excluding Disrupted Days)
         Ne is the expected number of business days in the contract‟s life (normally from the business day following the futures contract‟s listing day up to and including the Expiry
         Day, including Disrupted Days). This is fixed from the listing day
         n is the number of Observation Days to date (normally. from the business day following the futures contract‟s listing day up to and including the day of Daily Settlement,
         excluding Disrupted Days)
         RV is the Realized Variance; IV is the Implied Variance

                                                  2
                          n    p t 
                          Ln p 
                                      
                                                                            IV 
                                                                                    2 
                                                                                      
                                                                                                 P i ( K i 1  K i )   C i ( K i  K i 1)   10 ,000
                                                                                                                                              
                        t 1
                               t 1  
                                                                                  T 
                                                                                                       Ki
                                                                                                             2
                                                                                                                                 Ki
                                                                                                                                     2        
                                                                                                                                              
           RV    252                                 10 ,000
                                     n


                                            Where:
                                                                  T is the actual number of Observation Days remaining (i.e. excluding known Disrupted Days), until maturity of
                                                                  the Variance Futures, divided by 252
                                                                  Ki is the exercise price of the option being considered
                                                                  Pi is the premium of the out of the money put being considered
                                                                  Ci is the premium of the out of the money call being considered




                                                                                         23
Appendix 3 - Formulas
  Conversion of swap monetary exposure (per volatility point) to a “vega per lot”
  exposure

  The approximate vega exposure of a single variance futures contract is calculated using:

                                                              2  VPV 
Where:
                        Vega _ per _ lot 
                                                        var  1  var  1
         var is the futures contract traded variance level
         VPV is the variance point value which is either £50 for variance futures on FTSE 100 or €50 for variance futures on AEX and CAC 40



  Conversion to number of futures contracts
                                                NV               Ne
                Number_ contracts_ (r)                      ( Na  n)
                                          vega _ per _ lot 
Where:
         r is the number of contracts to be traded
         NV is notional volatility point exposure (e.g. £100,000)
         Na is the actual number of Observation Days in the contract's life (normally from the business day following the futures contract's
         listing day up to and including the Expiry Day, excluding Disrupted Days)
         Ne is the expected number of business days in the contract‟s life (normally from the business day following the futures contract‟s
         listing day up to and including the Expiry Day, including Disrupted Days). This is fixed from the listing day
         n is the number of Observation Days to date (normally from the business day following the futures contract‟s listing day up to and
         including the day prior to the Trade Date, excluding Disrupted Days)




                                                                   24
Appendix 3 - Formulas
Trade level for futures contracts with accrued RV
                                      ( RV  n )  ( IV  ( Na  n) )
           Trade level (TL) 
Where:                                              Ne
         RV is the realized variance
         IV is the implied variance
         Na is the actual number of Observation Days in the contract's life (normally from the business day following the futures
         contract's listing day up to and including the Expiry Day, excluding Disrupted Days)
         Ne is the expected number of business days in the contract‟s life (normally from the business day following the futures
         contract‟s listing day up to and including the Expiry Day, including Disrupted Days). This is fixed from the listing day
         n is the number of Observation Days to date (normally from the business day following the futures contract‟s listing day up to
         and including the day prior to the Trade Date, excluding Disrupted Days)



 Payoff of Variance Futures
            Payoff  r  VPV  (EDSP - TL )

Where:
         r is the number of contracts traded
         VPV is the is the variance point value which is either £50 for variance futures on FTSE 100 or €50 for on AEX and CAC 40
         EDSP is the final value for the variance futures contract
         TL is the futures contract trade level in variance points




                                                            25
Appendix 3 – Formulas, definitions

 “Business Day” means a day on which the relevant stock exchange and relevant derivatives exchange is
 open for business and the Index Provider published the level of the index

 “Disrupted Day” means any expected business day in respect of which exchange officials have
 determined that: (a) the Index Provider for any reason has not calculated or published, or will not calculate
 or publish, the Closing Index Value; and/or (b) the relevant stock exchange and/or relevant derivatives
 exchange has failed to open for trading during its regular trading session; and/or (c) a Market Disruption
 Event has occurred

 “Observation Day” means each expected business day that is not a Disrupted Day during the Observation
 Period

 “Observation Period” means the period from, but excluding, the Observation Start Date, and until and
 including the Valuation Date

 “Observation Start Date” means the third Friday of the month in which the relevant contract month was
 first made available for trading, provided a Closing Index Value is published on that day; otherwise, it shall
 be the last business day prior to such third Friday on which a Closing Index Value was published

 “Valuation Date” means the third Friday of the relevant contract month, except if at the time that the
 contract month was made available for trading the Expiry Day was determined to be a day other than the
 third Friday in which case the Valuation Date shall be such day

 Further definitions, including Market Disruption Events, are available in the Contract Specifications




                                                                26
Appendix 4 - Expiry Cycle – Sep 06




    Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                               27
         Appendix 4 - Expiry Cycle – Dec 06

                     Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08



Mar-08     Jun-08




          Note that „new‟ contract months are introduced on the morning of the expiry day
          of the front month contract




                                                                28
Appendix 4 - Expiry Cycle – Jan 07

       Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                 29
Appendix 4 - Expiry Cycle – Feb 07

       Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                 30
Appendix 4 - Expiry Cycle – Mar 07

       Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                 31
Appendix 4 - Expiry Cycle – Apr 07

      Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                   32
Appendix 4 - Expiry Cycle – May 07
      Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                   33
Appendix 4 - Expiry Cycle – Jun 07
      Sep 06 Oct Nov Dec 06 Jan Feb Mar 06 Apr May Jun 07 Jul Aug Sep 07 Oct Nov Dec 07   Jan Feb Mar 08




                                                    34

				
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