Variance Futures

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Variance Futures

• Variance Futures on Bclearfrom 15 December 2006
• Version 1.4
• 14 December 2006

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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

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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

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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

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Variance Swaps vs. Variance Futures

• Variance Swaps
• Flexible start dates
• Typically quarterly expiries
• At trade initiation value of contract is 100
  implied variance regardless of trade date
• Payout /notional variance x ((realized vol)2
  -(implied vol)2 )
• Non-standardised contracts

• Variance Futures
• Fixed start dates
• At trade initiation value of contract is 100
  implied variance only if traded on the listing
  day of contract or the following day
• 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 payoff of variance swap (see Appendix
  3)
• Standardised contract specifications
• First cleared, on-exchange solution with central
  counterparty
• - Disruption days governed by Exchange rules
  (based on ISDA rules)

ISDA is a registered trademark of the
International Swaps and Derivatives Association,
Inc.
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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)

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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

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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

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Variance Futures Fair ValueValue of Variance
Future during life of contract
At maturity 100 Realized
Futures first listing date 100 Implied
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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)

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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

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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
  contracts life) (realized variance from the
  trade date to the maturity date x proportion of
  time of the contracts life)
• (169 x (25/252) 324 x (227/252) 308.5
  (realized volatility for the contracts 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 contracts 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

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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

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Fees
Exchange transaction fees and LCH.Clearnet Ltd
clearing and cash settlementfees are as follows
Cash Settlement fee caps are applied to the total
expiring volume at TRS account level (i.e. House,
non-Segregated, Segregated)
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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 contracts 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

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Variance Futures Trade entry
User enters number of futures contracts
User enters expiry date here. Variance futures
expire on 3rd Friday of quarterly expiry month
User enters total variance here
Local Vega Approximation, Remaining Days,
Realized Variance, Implicit (Implied) Variance
are automatically calculated by Bclear
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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_at_liffe.com
• Your Account Manager

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Appendices

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

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

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Appendix 2 Margin rates
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Appendix 3 - Formulas

• Exchange Delivery Settlement Price (EDSP)
• - EDSP will be realized variance only
• Where
• 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 contracts life (normally from the business
  day following the futures contracts 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 t1, 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 t1, pt-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

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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
• Where
• 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 contracts life (normally from the business
  day following the futures contracts 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 contracts listing day up to and
  including the day of Daily Settlement, excluding
  Disrupted Days)
• RV is the Realized Variance IV is the Implied
  Variance

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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
• Where
• 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
• Where
• r is the number of contracts to be traded
• NV is notional volatility point exposure (e.g.
  100,000)

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Appendix 3 - Formulas

• Trade level for futures contracts with accrued
  RV
• Where
• 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 contracts life (normally from the business
  day following the futures contracts 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 contracts listing day up to and
  including the day prior to the Trade Date,
  excluding Disrupted Days)
• Payoff of Variance Futures
• 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

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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

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Appendix 4 - Expiry Cycle Sep 06
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Appendix 4 - Expiry Cycle Dec 06
Note that new contract months are introduced on
the morning of the expiry day of the front month
contract
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Appendix 4 - Expiry Cycle Jan 07
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Appendix 4 - Expiry Cycle Feb 07
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Appendix 4 - Expiry Cycle Mar 07
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Appendix 4 - Expiry Cycle Apr 07
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Appendix 4 - Expiry Cycle May 07
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Appendix 4 - Expiry Cycle Jun 07
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