Interest Rate PortfolioBond futures and options

Euronext refers to Euronext NV and any company which is at least a 50% owned subsidiary of Euronext NV.All proprietary rights and interest inthis publication shall be vested in Euronext and all other rights including, but without limitation, patent, registered design, copyright, trademark,service mark, connected with this publication shall also be vested in Euronext. LIFFE CONNECT® is a trademark of LIFFE Administration andManagement and is registered in Australia, Hong Kong, Singapore, the United States, Japan, the United Kingdom and as a European CommunityTrade Mark. No part of this publication may be redistributed or reproduced in any form or by any means or used to make any derivative work(such as translation, transformation, or adaptation) without written permission from Euronext.

Euronext shall not be liable (except to the extent required by law) for the use of the information contained herein however arising in anycircumstances connected with actual trading or otherwise. Neither Euronext, nor its servants nor agents, is responsible for any errors oromissions contained in this publication.This publication is for information only and does not constitute an offer, solicitation or recommendationto acquire or dispose of any investment or to engage in any other transaction.All information, descriptions, examples and calculations containedin this publication are for guidance purposes only and should not be treated as definitive.

Those wishing either to trade futures and options contracts on Exchanges within the Euronext Group, or to offer and sell them to others shouldestablish the regulatory position in the relevant jurisdiction before doing so.

Euronext.liffe refers to the combined derivatives operations of Euronext and LIFFE. It comprises:

l Euronext Amsterdam Derivative Markets, which is a regulated market under Dutch Law;l Euronext Brussels Derivatives Market, which is a regulated market under Belgian Law;l Euronext Lisbon Futures and Options Market, which is a regulated market under Portuguese Law;l LIFFE Administration and Management, which is a Recognised Investment Exchange under English Law;l MATIF and MONEP, which are regulated markets under French Law.

All are regulated markets under the European Union’s Investment Services Directive.

Euronext NVPO Box 191631000 GD AmsterdamThe NetherlandsTel +31 (0)20 550 4444

For more information about Euronext.liffe’s Bond products please contact:

Interest Rate Derivatives:Tel: +44(0)20 7379 2222

Fax: +44(0)20 7929 1050

Email: bonds@liffe.com

Web: www.euronext.com

Further information

Introduction 1

Contract specifications 4• Long Gilt futures 4• Option on Long Gilt futures 6• Japanese Government Bond (JGB) futures 7

Pricing Bond futures 8• Principle of forward pricing 8• The price (conversion) factor 8• Invoice amount formula 8• Cash and carry arbitrage 9• Implied repo rate calculation 9• Basis analysis example 10

Option pricing 12• Option value determination 12• Types of volatility 14• Option sensitivities 15• Summary 18

Trading Gilt futures and options 19• Spread trading 22• Hedging 22• Sell futures 23• Buy puts 23• Sell calls 24• Using futures in asset allocation 25

Accessing futures and options on the Euronext.liffe market 27• LIFFE CONNECT® 27• Wholesale trading facilities 30• Euronext.liffe’s block trading facility 30• Euronext.liffe’s basis trading facility 31

Contents

Margining 33• The role of the clearing house 33• SPAN® margining requirements 34

Appendix A• Long Gilt futures contract price factor 36

Appendix B• Quote vendor contract codes 39

Appendix C• Further reading 40

Further information Inside back cover

Volatility and uncertainty are ever present in today’s financial markets, not least in the interest ratemarkets. In the face of this type of uncertainty, traders, treasurers and fund managers are increasinglyadvised to consider methods of managing their exposure to sharp movements in financial markets.

Futures and options were conceived for the purpose of managing risk, which in turn can be translatedinto the protection of prices. Futures and options, through their versatility, offer significant advantagesas strategic financial instruments.They help reduce costs, enhance returns, and manage interest raterisk with greater certainty, precision and economy.

Additionally, market participants, when using futures, can benefit from less restrictive regulatoryconstraints pertaining to capital requirements, facilitating more efficient use of available capital.

This publication provides the reader with a full overview of the Bond Futures and Options availablefor trading on LIFFE CONNECT® in addition to a firm understanding of the basic principles behindthe use of the contracts.

Bonds and their characteristicsIn layman’s terms, a bond can be thought of as an IOU exchanged between two parties. It is also anIOU designed to be easily transferred in the secondary market.Technically it is defined as a debtsecurity. Bonds are issued by a number of different types of institutions, such as Governments, PublicCorporations and Supranational agencies.These institutions are known as issuers and they typicallyissue a bond in order to raise money to invest in long-term capital projects.

When you buy a bond at issue in the primary market, you are lending money to the issuer. In return,the issuer will pay you, the lender, a specified rate of interest, known as the coupon, on the amountyou lend over the lifetime of the bond and repay the principal amount upon “maturity” of the bond.When you sell on the bond in the secondary market the rights to coupon payments and principalrepayment are transferred to the new owner of the bond. Depending on the issuer, coupon paymentis usually either semi-annual or annual.

Bonds are priced based on a nominal value of 100 percent. Prices may fluctuate above or below 100throughout the lifetime of the bond.This is due mainly to the interest rates prevailing in the secondarymarket relative to the value of the bond’s coupon payments.As the price of the bond fluctuates aboveor below 100, the coupon payment is not exactly the return on investment.The return you receive isknown as the yield and the calculation is based on the coupon rate, time to maturity and market price.

The prices normally quoted for bonds are referred to as ‘clean’ prices, meaning they do not includethe interest which has accrued on the bond since the last coupon payment.When the bond actuallychanges hands, the actual amount paid will be the ‘dirty’ price, which includes accrued interest.

The UK Government Bond marketBonds issued by the UK Government are commonly known as Gilts.They are issued to themarketplace entirely through an auction process which is held by the Debt Management Office(DMO), a division of the UK Treasury.The UK Debt Management Office was created in April 1998 asan executive agency of Her Majesty’s Treasury, with the brief of minimising the government’s financingcosts. Gilts are issued to finance the Central Government’s Net Cash Requirements and to refinancematuring debt. Gilt auction dates are published up to a year in advance.

1

Introduction

Gilts have a wide range of maturities, and are categorised as shorts (1-7 years) mediums (7-15 years)and longs (over 15 years).Almost all Gilts pay interest, also known as a dividend or coupon, on a six-monthly basis.

Gilts are priced in decimals and quoted per £100 of principal. Seven business days before the couponpayment date, Gilts begin to trade ‘ex-dividend’ or ‘ex-div’. If the Gilt is bought whilst it is ‘ex-div’, thebuyer gives up the right to receive the following dividend payment and is compensated by the selleraccordingly.Therefore, from the ex-dividend date until the coupon payment date, the accrued interestwill be negative.

There is an established group of firms in the market known as Gilt-Edged Market Makers (GEMMs).GEMMs are primary gilt dealers who participate in all DMO issuance auctions and also providecontinuous 2-way prices to the secondary market.They may deal with each other as well ascustomers.To preserve pre-trade anonymity, GEMMs often use inter-dealer brokers (IDBs) asintermediaries to their trades.

The German Government Bond marketThe issuance of German Government Bonds is the responsibility of the German Finance Agency,known as Bundesrepublik Deutschland Finanzagentur, on behalf of the German Government. Bondswith lifetimes, or maturities, of 2, 5, 10 and 30 years are issued. Interest payment for these bonds isannual and maturities are fixed.The 2, 5, 10 and 30 year German issues are known respectively asFederal Treasury notes (Bundesschatzanweisungen or “Schätze”), Five-year Federal notes(Bundesobligationen or “Bobls”) and Federal bonds (Bundesanleihen or “Bunds”). Bunds, Bobls andSchätze are brought to the market through an auction process.

The Japanese Government Bond marketThe Japanese Government Bond (JGB) market is the world’s largest.The 10 year sector of the marketis by far the largest in terms of issuance. Euronext.liffe’s JGB future is based on this segment of themarket. JGBs are issued through a US style ‘Dutch Auction’ and offered to an underwriting syndicate.Interest payments on JGBs are semi-annual.

International bond market conventionsThe following table provides an overview of the key features and relevant information relating to theunderlying bond markets covered by Euronext.liffe contracts.

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Country Coupon Day Count Settlement Relevant web sites

United Kingdom Semi-annual Actual/Actual Usually T + 1 www.hm-treasury.gov.ukwww.dmo.gov.ukwww.bankofengland.co.uk

Germany Annual Actual/Actual Usually T + 2 www.deutsche-finanzagentur.dewww.bundesbank.de

Japan Semi-annual Actual/365 Usually T + 3 www.mof.go.jpwww.boj.or.jp

Bond futures and optionsFutures:A deliverable futures contract is a legally binding obligation to make or take delivery of a specifiedinstrument at a fixed date in the future, at a price agreed at the time of dealing. In addition all futurescontracts are exchange traded securities. In the case of bond futures, the seller must deliver to thebuyer an agreed amount of an eligible bond from a list of deliverable bonds at the agreed price.The buyer of the futures contract will take delivery from the seller.These two parties are knownas holders of Long and Short positions respectively.

Options:An option contract is a legally binding agreement which bestows upon the buyer a right, but not anobligation, to take (call) or make (put) delivery of a specified instrument at a fixed date in the future,at a price agreed at the time of dealing.The specified instrument which must be ‘called’ or ‘put’ by thebuyer or seller of a Euronext.liffe Bond Option, is the relevant Bond futures contract.

Euronext.liffe Bond futures and optionsEuronext.liffe offers a number of Bond futures and options contracts that provide exposure to theBritish and Japanese Government Bond markets.

The table below presents an overview of the available contracts

3

Contract Currency Futures Options

Long Gilt Sterling Yes Yes

JGB Japanese Yen Yes No

The contract specifications provided below are correct as of February 2006. Please refer to theEuronext.liffe website (www.euronext.com/derivatives) for the most up to date versions.

Long Gilt futures

Unit of trading £100,000 nominal value notional Gilt with 6% coupon

Delivery months March, June, September, December, such that the nearest three delivery monthsare available for trading

Quotation Per £100 nominal

Minimum price movement 0.01 (£10)(Tick size and value)

First notice day Two business days prior to the first day of the delivery month

Last notice day First business day after the last trading day

Last trading day 11.00 Two business days prior to the last business day in the delivery month

Delivery day Any business day in delivery month (at seller’s choice)

Trading hours 08.00 – 18.00 London Time

Trading platform:l LIFFE CONNECT® Trading Host for futures and options.l Algorithm: Central order book applies price-time priority trading algorithm.l Wholesale trading facilities: Asset allocation, block trading, basis trading.Exchange delivery settlement price (EDSP): The LIFFE market price at 11.00 on the secondbusiness day prior to the Delivery Day.The invoicing amount in respect of each Deliverable Gilt is tobe calculated by the price factor system.Adjustment will be made for full coupon interest accruing asat Settlement Day.Contract standard: Delivery may be made of any gilts on the List of Deliverable Gilts in respect ofa delivery month, as published by the Exchange on or before the tenth business day prior to the FirstNotice Day of such delivery month. Holders of long positions on any day within the Notice Periodmay be delivered against during the delivery month.All gilt issues included in the List will have thefollowing characteristics:l having terms as to redemption such as provide for redemption of the entire gilt issue in a single

installment on the maturity date falling not earlier than 8.75 years from, and not later than 13 yearsfrom, the first day of the relevant delivery month;

l having no terms permitting or requiring early redemption;l bearing interest at a single fixed rate throughout the term of the issue payable in arrears semi-

annually (except in the case of the first interest payment period which may be more or less thansix months);

l being denominated and payable as to the principal and interest only in pounds and pence;l being fully paid or, in the event that the gilt issue is in its first period and is partly paid, being

anticipated by the Board to be fully paid on or before the Last Notice Day of the relevantdelivery month;

l not being convertible;l not being in bearer form;l having being admitted to the Official List of the London Stock Exchange;

4

Contract specifications

l being anticipated by the Board to have on one or more days in the delivery month an aggregateprincipal amount outstanding of not less than £1.5 billion which, by its terms and conditions, ifissued in more than one tranche or tap or issue, is fungible.

5

Option on Long Gilt futures

Unit of trading One Long Gilt futures contract

Expiry months March, June, September, December (nearest two available for trading) plus twoadditional serial months, such that four expiry months are available for trading,which include the nearest three consecutive calendar months

Quotation Multiples of 0.01

Minimum price movement 0.01 (£10)(Tick size and value)

Exercise day Exercise by 17.00 on any business day, brought forward to 10.45 on the lasttrading day

Last trading day 10.00 Six business days prior to the first day of the expiry month

Expiry Exercise by 10.45 on the last trading day

Delivery day Delivery on the first business day after the exercise day

Trading hours 08.02 – 16.18 London Time

Trading platform:l LIFFE CONNECT® trading host for futures and options.l Algorithm: Central order book applies a pro-rata trading algorithm, but with priority given to

the first order at the best price subject to a minimum order volume and limited to maximumvolume cap.

l Wholesale trading facilities: block trading, basis trading.Contract standard: Assignment of one Long Gilt futures contract for the expiry month at theexercise price.The futures delivery month associated with each option expiry month shall be:March in respect of January, February and March expiry months;June in respect of April, May and June expiry months;September in respect of July,August and September expiry months;December in respect of October, November and December expiry months.Exercise price intervals: £0.50 eg £102.00, £102.50 etc.Introduction of new exercise prices: Thirteen exercise prices will be listed for each new series.Additional exercise prices will be listed when the Long Gilt futures contract settlement price is within£0.25 of the sixth highest or lowest existing exercise price, or as deemed necessary by the Exchange.Option premium: The contract price is not paid at the time of purchase. Option positions, as withfutures positions, are marked-to-market daily giving rise to positive or negative variation margin flows.If an option is exercised by the Buyer, the Buyer is required to pay the original contract price tothe Clearing House and the Clearing House will pay the original option price to the Seller on thefollowing business day. Such payments will be netted against the variation margin balances of Buyerand Seller by the Clearing House.

.

6

Japanese Government Bond (JGB) futures

Unit of trading ¥100,000,000 nominal value notional long term Japanese government bond with6% coupon

Delivery months March, June, September, December, such that three delivery months are availablefor trading

Quotation Per ¥100 face value

Minimum price movement 0.01 (¥10,000)(Tick size and value)

Last trading day 16.00 One business day prior to Tokyo Stock Exchange last trading day

Delivery day Next business day*

Trading hours 07.001 – 16.00 London Time

Trading platform:l LIFFE CONNECT® trading host for futures and options.l Algorithm: Central order book applies price/time priority trading algorithm.l Wholesale Trading Facilities: Asset Allocation, Block Trading, Basis Trading.Contract standard: *All open positions on Euronext.liffe at the close of a business day will beclosed out automatically at the first subsequent opening price on the Tokyo Stock Exchange for thesame delivery month, and cash settlement made accordingly through variation margin. Unless deferredas a result of there being no TSE opening price (eg in the event of a TSE holiday), settlement will be onthe next business day.Price limit: (1) ¥2.00 from Tokyo Stock Exchange closing price. If limit is hit, price limits are removedone hour later for the remainder of the day. (2) No limit during the last hour of trading on each day.

1 The JGB Contract opens at 08.00 on Tokyo Stock Exchange Holidays.

7

The prices at which futures contracts trade is fundamentally related to the prices which prevail forbonds in the underlying bond market.This connection is accomplished through the potential forarbitrage between the cash bond and futures market.

Principle of forward pricingFutures pricing is the result of an analysis of the value of owning an asset today, and having available aknown price at which the asset might be sold on some future date. For example, if one were to be inpossession of an ounce of gold or a barrel of oil it would be rational to consider the value that mightbe acquired from the sale of that asset in today’s cash market, compared to the value to be acquiredfrom the sale of that asset at some different price at some future date.As a cash bond/futures arbitragecalculation, this analysis takes the form of looking at the possibility of purchasing the asset in the bondmarket today and then selling that asset forward through the futures delivery and clearing process.

This relationship can be expressed as:

= + –

Delivery basketUnderlying bond futures, and unlike various other types of futures such as stock futures andcommodity futures, there is a list of different bonds which can be delivered when the contract expires.This list is commonly known as a basket.The basket contains different bonds which vary in theircharacteristics but match a set of criteria specified by the Exchange. Most often the bond will differin its coupon and time to maturity.The specified criteria for the Bond futures contract listed byEuronext.liffe can be found in the Contract Specifications.

The price (conversion) factorDue to the non-homogeneous nature of the bonds contained within the deliverable basket, each bondis assigned a factor which is applied to the final invoice price calculation.

This price factor is the mechanism which brings the maturity and coupon differences of thedeliverable bonds onto a common base and is intended to make all of the bonds equally attractivefor delivery. In essence, a bond’s price factor is the price, per 1 nominal, at which the deliverablebond would yield the notional coupon on the delivery day, or the first day of the delivery month inthe case of Long Gilt futures.

Invoice amount formulaThe process of delivery established by the Exchange provides the facility for a trader holding a shortfutures position, to deliver any bond from the list of deliverable bonds, via LCH.Clearnet on thecontract’s delivery date.The proceeds of that delivery are determined by the final Exchange DeliverySettlement Price (EDSP) multiplied by the delivered bond’s price factor and adjusted for accumulatedaccrued interest at delivery.The proceeds of the sale resulting from a single contract varies with bondthe holder of the short position elects to deliver, and is called the invoice amount

Invoice amount = (EDSP x scaling factor x price factor) + accrued interest

The EDSP is quoted per 100 nominal.The scaling factor adjusts for the nominal value size of thefutures contract. In the case of the Long Gilt (£100,000), the scaling factor is 1,000.

incomefrom cashbond sale

cost offinancing

Cashbondprice

FuturesPrice

8

Pricing Bond futures

Cash and carry arbitrageA curious trader would naturally want to see how the price of a bond at delivery (EDSP) mightcompare to the current market price of those bonds. Specifically, the trader might wish to know ifthere might be a profit to be made from buying a bond from the deliverable basket today, then holdingit for a specific period of time, whilst simultaneously fixing a selling price for the same bond forwardvia the futures market.

This process of buying a bond and locking in a forward selling price is akin to achieving a lending rate.The term associated with this action is known as a cash and carry analysis.The rate achieved is calledthe implied repo rate.Alternatively the trader may decide to short a cash bond today and buy it backvia the futures market.This action would be akin to achieving a borrowing rate, and is known as areverse repo.

Implied repo rate calculationThe following formula may be used to calculate the implied lending rate:

where = Clean cash price of bond at delivery (futures price x price factor)

= Current clean market price of bond

= Accrued interest of bond at delivery per £100 principal

= Accrued interest of bond for current settlement per £100 principal

= Intervening coupon

= Actual number of days from settlement to delivery

Example:Trade date: 26 Jan 04Settlement date: 27 Jan 04Delivery date: 31 March 04Holding period: 64 daysBond: 8% 27 Sep 2013Current bond price 124.74Accrued interest at settlement 2.6813Actual repo rate ~4%Current futures price 108.56Price factor 1.1439664Bond price at delivery 108.56 x 1.1439664 = 124.188992Accrued interest at delivery 0.086957Intervening coupon 4

dCP

sCP

dAI

sAI

IC

sdDays −

dCP

sCP

dAI

sAI

IC

sdDays −

dCP

sCP

dAI

sAI

IC

sdDays −

dCP

sCP

dAI

sAI

IC

sdDays −

dCP

sCP

dAI

sAI

IC

sdDays −

dCP

sCP

dAI

sAI

IC

sdDays −

( ) ( )( ) sdss

ssdd

Daysx

AICP

AICPICAICP

−++−++ 365

9

(124.74 + 2.6813) x 3.83% implied repo rate64365(124.188992 + 0.086957 + 4) − (124.74 + 2.6813) =

Using the implied repo formula:

The cheapest to deliverThe calculation of return on investment tells the trader the return associated with buying a bondand holding it to delivery.The bond with the highest implied repo rate offers the greatest profit(or smallest loss) as a percentage of funds invested of all the bonds available for arbitrage.This bondis referred to as the cheapest to deliver (CTD) bond. By comparing the implied repo rate for eachbond with a comparative borrowing rate for the same duration (actual repo), a trader is able to seeif any arbitrage potential exists. In other words, if the implied repo rate (synthetic lending rate) isgreater than a corresponding actual repo rate (borrowing rate) then there is an arbitrage profit tobe had.Typically, as the above example shows, there is no arbitrage to be had, as the actual reporate was around 4% in this case.

Considering the cost of fundsA trader acting as a pure arbitrageur is unlikely to be operating with a large pool of money. Instead thetrader will be looking to borrow funds to execute the transaction.The cost of these funds will impactthe profitability of the arbitrage and the trader will require a calculation of the profit incorporating thecost of funds.

Financing costs and carry returnThe cost associated with holding a bond to delivery is the financing cost.This cost is the result ofboth the interest rate charged in the transaction as well as the holding period.This financing cost iscompared to the coupon income that is earned.The difference between coupon income and thefinancing cost is called ‘carry basis’. If the bond’s coupon income is greater than the cost of financing,the position is said to have positive carry, if not then it has negative carry.

Basis analysis exampleThe cost of financing a cash and carry position is a simple money market calculation and is given bythe following formula:

Amount financed = CP + AI Financing rate = Actual Repo RateDays to delivery = Days

Using the trade information from the previous example we can calculate the financing cost for thecash bond 8% 27 Sep 2013.

Cost of finance = (124.74 + 2.6813) x 4.01% x 64/365 = 0.895929

Coupon income is the amount of interest earned from settlement to delivery date.

Coupon income = 1.406593

365 days to delivery

xFinancing ratexfinancedAmount

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Carry basisCarry basis is the difference between coupon income and financing costs.Typically carry basis ispositive, reflecting the fact that the return from holding the bond (coupon income) will be greaterthan the financing costs (actual repo rate) for normal (positively sloped) yield curves.

Carry basis = coupon income – financing costs= 1.406593 – 0.895929= 0.5107

Gross basis is the difference between the cash bond price and the futures adjusted price.

Gross basis = cash bond price – (futures price x price factor)= 124.74 – (108.56 x 1.1439664)= 0.5510076

An arbitrageur given the above equations is now able to calculate the all in costs of a cash andcarry analysis.

Net basis = Gross basis – coupon income + financing cost= Gross basis – carry basis= 0.5510076 – 0.5107= 0.04 or 4 ticks

Net basisThe difference between the cost of borrowing (cost of funds) and the lending rate (implied repo)achieved through the cash and carry is known as net basis (value basis). Under normal conditions, netbasis is negative, and there is thus no single bond arbitrage to be made (it is convention to show thisloss however as a positive number). In this example the potential arbitrageur would lose 4 ticks if hewere to perform the cash and carry transaction delivering the example bond into the futures shortposition. Part of the explanation for the net basis being negative is the optionality contained withinthe bond futures delivery process and hence reflected in the bond futures price.

Delivery optionIn a simple world, gross basis should equal carry basis, in other words the net difference (basis)between the price of the cash bond today and the futures adjusted price should be zero.Typicallythe actual futures price will trade at a price slightly below its fair value. One reason for this is thatthe seller of the futures contract has certain rights, such as choice of bond to deliver and the dayin the delivery month on which to deliver.This right to choose is sometimes valuable and is calledthe delivery option.

The value of the delivery option principally arises from the possibility of a change in the cheapestto deliver, which can happen if overall yield levels in the cash market move significantly.A futures longhas given away the delivery option to the short at the time of trade, so the buyer of the futurescontract has to be compensated.This compensation takes the form of a reduced futures price.Thus we can say that the net basis reflects a series of in-built options which are subject to changeover the life of the futures contract.

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Option value determinationAn option bestows upon the buyer a right to buy (call) or sell (put) the underlying futures contract ata pre-determined price on or before (American style) a final expiry date. Buyers of options have rightsand sellers have obligations.

Price distributionThe pay-off characteristic of an option depends not so much upon the price of the underlying futurescontract today, but rather, what the pattern of future price distributions is likely to be between nowand option expiry. It is this distribution of future prices that dictates the likelihood that the option willbe in-the-money, and by what extent at expiry.

The theory of option pricing centres on the concept that the ‘fair option price’ is based upon a valuewhich will allow a hedger to precisely offset any exposure they may have in the underlying market.Many option pricing models prevail in the market today, encompassing very detailed calculations.What follows is a succinct explanation, in general terms, of how an option premium is derived.

Option valueThe price or premium (value) on an option is determined by the following parameters which areentered into an option pricing model1.

The first three inputs into the model are easily observable in the market place and can be said tobe objective.The fourth input into the option pricing equation, volatility, is subjective.This is theindividual trader’s view on what the distribution of the future prices will be between now andexpiry of the option.

12

Option pricing

1 Euronext.liffe options on bond futures operate on a delayed payment of premium basis.This means that there is no need toincorporate an interest rate element into the pricing model.

Exercise priceKnown

Current futures price Known

Time to expiryKnown

Expected volatility Unknown

Option pricing model

Optionpremium

Determining the future price distributionThe illustration below shows in simple terms how an options price may be calculated over a singletime period.The following method is based upon the binomial pricing concept.

100 call option value – single time period105 (5)

100(2.5)

95 (0)

In this example the futures price is conditioned to move up or down in steps of 5 points and has a50% chance of either being in-the-money or out-the-money at expiry.The value of the 100 call optionunder the above scenario equates to 2.5.This is the sum of the two possible outcomes.That is, if thefutures price at expiry is 105, the 100 call option is worth 5, but as there is only a 50% probability ofthis occurring, the value is calculated as 5 x 50% = 2.5.The value of the 100 call option is zero if thefinal futures price is at, or below 100.

Applying the same conditions as before, we now increase the time period to three, this has the effectof increasing the distribution of probable outcomes, thus increasing the value of the starting 100 calloptions price from 2.5 to 3.75.This is intuitively correct as there has been an increase in the chancesof the option being in-the-money at expiry.

100 call option value – three time periods

The value of the 100 call option under the revised three time period scenario is now 3.75. In order tocalculate this premium the model requires you to work backwards to asses the value of the option ateach branch of the lattice tree. For example at t3 (expiry) with the futures price at 115, the value of the100 call is worth 15, this is simply the difference between the futures price and the option exerciseprice (115 -100 = 15).With the future at 105 the option is worth 105 – 100 = 5 at expiry etc.

115(15)

110(10)

105 105(6.25) (5)

Future 100100 (2.5)(3.75) 95 95

(1.25) (0)90(0)

85(0)

t0 t1 t2 t3

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The premium of an option that is in-the-money at expiry (t3) will comprise solely of intrinsic value.Options that are at or out-the-money at expiry have zero value.This is illustrated above. Prior toexpiry in-the-money options may contain both intrinsic and time value.At and out-the-money optionsprior to expiry will contain only time value ie no intrinsic value.

At t2 (one period before expiry), if the futures price is trading at 110 we can calculate the 100 calloption value as being 10.That is the sum of the two possible outcomes for the futures price (115 or105).We already know the value of the option prices at 115 (15) and 105 (5) Therefore, the value ofthe 100 call option can be calculated {(15x50%=7.5) + (5x50%=2.5)} = 10.

The process is repeated throughout the lattice so at each stage it is possible to value the option overtime. Just to complete the picture, at t1 with the future at 105, the option value will be {(10x50%=5) +(2.5x50%=1.25)} = 6.25.And finally at t0 the value of the 100 call is calculated as {(6.25x50%=3.125) +(1.25x50%=0.625) = 3.75.

We can conclude that an increase in time has the effect of increasing the range of possible futureprice outcomes. In other words, time and future price distributions are inexorably linked.The longerthe time remaining to maturity of an option, the greater the likelihood of the option being in-the-money at expiry.As a consequence of increased time to expiry, the option premium is higher (forcalls and puts) which reflects the compensation offered to the seller of the option for the increasedrisk of being exercised.

Types of volatilityThe likelihood of an option being profitable at expiry depends largely upon the time and the expectedfuture price distribution or volatility.Volatility is the term used by option traders to describe thepropensity of the futures price to move (either up or down) over a period of time.Volatility is one ofthe most important elements to be considered when trading options.This is explained by its highlysignificant influence on the option’s price.A large number of option trading strategies are centredon volatility expectations. Option volatility can be described using different measures:

Historic volatilityHistoric volatility is simply the observed futures price movements over a period of time.Although theprice movements are objective, the assimilation of the data can lead to subjective results. For example,in order to value a 3 month option, a trader may wish to review historic prices for the last 2 years andweight the findings according to his chosen preference.

Expected volatilityUsing historic volatility and taking into consideration events that may or may not occur in the futureallows the trader to derive an expected volatility which is clearly subjective. Expected volatility istherefore what the trader believes the futures price distribution will be between now and optionexpiry. Each trader will have their own interpretation of expected volatility.

Implied volatilityImplied volatility is the volatility needed in the option pricing equation to generate a given optionvalue.The given option price, which can be observed in the options market, represents a consensusview of volatility.The difference between implied volatility and expected volatility is what influencesthe decision to trade options for many participants.

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We can appreciate now that an increase in expected volatility and time has the effect of increasingoption premiums for both calls and puts.A fall in volatility and time has the opposite effect.

Option sensitivitiesThe option pricing model is not only useful for calculating an option’s price for today, but can beused to generate a series of option sensitivities (the Greeks).These sensitivities help inform a traderas to the likely change in an option’s value given a change in one or more of the various inputs intothe model.

DeltaThe delta of an option indicates how sensitive the option price is to a change in the price of theunderlying future. Knowing the delta of an option is useful for both hedging and trading purposes.The range of deltas for calls, puts and futures is shown below.

in-the- at-the- out-of-the-money money money

Calls +1 +0.5 0Puts -1 -0.5 0Long future +1Short future -1

Example of delta use – estimating a new option’s valueFutures price 10098 Call option price 0.25Delta 0.65

A trader is interested in knowing what the estimated new price of the option will be, should thefutures price move up by 1 full point (100 ticks).

To calculate the new option price we simply multiply the futures price movement by delta ie 100 ticksx 0.65 = 65 ticks.Therefore the estimated new option price is 0.25 + 0.65 = 0.90.

Example of delta use – hedging with optionsA trader is long a Long Gilt futures contract and wishes to hedge his position using options.How many at-the-money puts does he need to buy, in order to create a delta neutral position?

A long futures position has a delta of +1, so two at-the-money puts (-0.5) are required to create adelta neutral hedge.

Delta is very useful for estimating the change in the option value for a change in the price of theunderlying future. However, delta has its limitations. In an environment where the futures price movesby a considerable amount, delta will either, under or over estimate the real change in the value of theoptions position.

15

In particular, holders of long positions (puts/calls) would achieve greater than expected gains andlower than expected losses when the market moves significantly up or down. Conversely, holders ofshort positions would achieve lower than expected gains and higher than expected losses (as shownin the table below).This is because the option delta changes over time and as the option moves moreor less in or out-the-money (convexity effect). Gamma is a measure of the expected change in deltafor one unit change in the underlying futures price.

Delta impact on option prices for large movementsFutures up Futures down

Long call under estimate profit over estimate loss

Short call under estimate loss over estimate profit

Long put over estimate loss under estimate profit

Short put over estimate profit under estimate loss

The diagram illustrates a large fall in thefutures price from f1 to f2. Using delta aloneas represented by the tangent, the fall in thelong call premium would be shown as od1 to od2.In fact the true fall is less, ie a fall from od1 to o2.

GammaThe gamma of an option can be used to adjust for the inaccuracies of delta. In the above illustration,gamma will account for the discrepancy in estimated option price movements between od1 – od2

and od1 – o2.

Gamma can be used to estimate the new option delta as a result of a change in the underlying futuresprice. Gamma is expressed in deltas gained or lost for a full point move in the underlying price. Forexample, as the underlying price rises, an at-the-money call with a delta of 0.50 will now move in-the-money. If the gamma of the option is 0.2962, a trader can estimate the new delta for his option bysimply adding the gamma to his original delta.

optionprice

od1

o2

od2

f2 f1 futuresprice

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ExampleFutures price change +1.00 Call delta 0.50Gamma 0.2962

The new option delta would be 0.50 + 0.2962 = 0.7962.

For a long put at the same exercise price, the change in the option delta would be -0.50 + 0.2962 =– 0.2038 as a result of a rise in the futures price of one point. Long options have a positive gammaposition and short options have a negative gamma position.

From the above example we can appreciate that, as the underlying price changes the delta of an optionwill also change. Gamma can help an options trader to assess how quickly his option delta positionmay change. For example, an option trader may have a portfolio of options which collectively resultsin a near zero delta position. If however, the portfolio has a large gamma position, gamma is tellingthe trader that for even a small change in the futures price the net delta position could changedramatically generating huge gains or losses. If the position is to remain delta neutral the traderwill need to rebalance his position over time. Either options or futures may be used.

ThetaTheta is a measure of the change in the options price for a change in time. For example, an out-of-the-money call with a premium of 0.20 and 30 days remaining until expiry will exhibit decay in its valuewith all else remaining equal, simply through the passage of time.

If the theta of the option is 0.005670, then for each day that passes the option value will erode by0.005670. For example, a call worth 0.20 today will be worth 0.19433 tomorrow (20 ticks – 0.005670)and so on.

Theta works against both long call and put positions, but works in the favour of holders of shortoptions.Time value decay is the greatest for at-the-money options.

VegaVega is a measure of change in an options price for a change in volatility. It is usually represented as achange in option value given a full point change in volatility. For example, an option has a value of 2.19and a vega of 0.1652. If the volatility changes by 1% from 16% to 17% then the new option price willbe 2.36 (2.19 + 0.1652).

An increase in volatility is beneficial for long option positions but detrimental for short positions,whereas a fall in volatility is detrimental for long positions but beneficial for short positions.

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SummaryThe table below shows the direction of movement for various option and futures positions as a resultof a change in future price, time and volatility.

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Position delta gamma theta vega

Long future + n/a n/a n/a

Short future - n/a n/a n/a

Long call + + - +

Short call - - + -

Long put - + - +

Short put + - + -

Futures and options can be used in numerous ways either to generate profits or minimise losses whenprices change.A number of applications for bond futures and options are outlined below.

Speculative trading An investor who wishes to take an outright position in futures based on his view of the direction ofyields, can do so by buying or selling futures, depending on whether he expects yields at this part ofthe curve to rise or fall.As yields rise, prices fall and vice versa.

View – ‘Bullish’ Futures position – LongInvestors expecting the price of the futures to rise can enter into a long futures position which willprofit if the value of the futures at expiry is above the price paid now. If the price rises during thelifetime of the contract then the investor can close out (sell) his long position for a profit.The payoffprofile below shows how the profit increases as the price of the futures rises. If the futures price falls,the position begins to make a loss.

Option position – Long CallBy buying a call option investors can limit the loss on his position if prices fall, to the amount ofpremium paid.The upside is unlimited.The payoff profile, below, illustrates this.

Example:Day1Option Premium – 0.35Option Strike – 108.00Futures Price – 107.89

Day 2 Futures Price – 109.21Profit/Loss – 109.21-108.00-0.35 = 0.86

Price

0

Profit/Loss

Price

0

Profit/Loss

Trading Gilt futures and options

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Scenario 2 – A trader expects yields on 10 year gilts to rise and thus prices to fall.

View – ‘Bearish’Futures position – Short futureA short futures position will profit when prices fall and make a loss if prices rise.The payoff profilebelow illustrates this.

Option position – Long putAlternatively investors can buy a put option which will limit the maximum possible loss to the cost ofthe option.The upside is potentially unlimited.

Example:Day 1Option Premium – 0.15Option Strike – 108.55Futures Price – 108.86

Day 2Futures Price – 107.00Profit/Loss – 108.55-107.00-0.15 = 1.4

Price

0

Profit/Loss

Price

0

Profit/Loss

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View – NeutralOption position – Short callInvestors expecting yields to remain unchanged, or to rise slightly and thus the price to remainunchanged or fall slightly will sell a call option. If the prediction comes true, the option will expire out-the-money and thus not be exercised.The seller of the call profits from the premium earned. Howeverif the price rises, the potential loss is unlimited.The payoff profile, below, illustrates this.

Example:Day 1Option Premium – 0.35Option Strike – 108.00Futures Price – 107.89

Day 2 Futures Price – 107.79Profit/Loss – The buyer of the option will not exercise the option and it will expire worthless.The profit for the seller will be the premium.

Option position – Short putInvestors expecting yields to remain unchanged, or to fall slightly and thus the price to remainunchanged or rise slightly will sell a Put option. If the prediction comes true, the option will expireout-the-money and thus not be exercised.The seller of the put profits from the premium earned.However if the price falls, the potential loss is unlimited.The payoff profile, below, illustrates this.

Example:Day 1Option Premium – 0.15Option Strike – 108.55Futures Price – 108.86

Price

0

Profit/Loss

Price

0

Profit/Loss

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Day 2Futures Price – 108.88

Profit/Loss – The buyer of the option will not exercise the option and it will expire worthless.The profit for the seller will be the premium.

Spread tradingSpread trading involves taking opposing positions in more than one futures contract.The spreadcan be intra-commodity (between futures contracts with the same underlying instrument), orinter-commodity (futures with different underlying instruments).

Intra-commodity spreads, also known as calendar spreads, involve taking a simultaneous long and shortposition in futures with the same underlying instrument but in different expiry months.The traderexpects that the price difference between the two contracts will change, either widen or narrow.Along spread is when the near calendar month is purchased and the far month is sold.The opposite isthe case for a short calendar spread.The risk associated with a spread position is much lower than anoutright position as any loss in one contract may be largely offset by a gain in the opposing position.

Example:January 2005Long Gilt March 05 future – 108.10 Long Gilt June 05 future – 107.66

Buy March 05/June 05 calendar spread at price 0.44

February 2005Long Gilt March 05 future – 108.25 Long Gilt June 05 future – 107.51

Sell March 05/June 05 calendar spread at price 0.74

Profit/Loss – 0.30 (0.74-0.44)

HedgingHolders of long or short positions in cash bonds will want to protect their investments from adverseprice movements.They can do so by buying or selling futures.

A bond portfolio manager is concerned about the rising trend in yields.To protect the portfolio heconsiders the possibility of hedging the fund with either futures or options.Three alternatives are tosell futures (locking in a single fixed value), buy puts (securing a minimum value), or sell calls (achievinga maximum value).The diagram below compares the expiry profiles of the three alternatives.

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Expiry profiles of alternative hedging strategies

The construction and explanations of each of the three expiry profiles are shown below.

Sell futuresThe futures hedge leaves the fund manager completely flat.The advantage of this strategy is that thereis no premium outlay, but it does mean that if yields do not rise as expected but fall, the portfolio willnot benefit from this movement.

Buy putsBuying puts allows the fund manager to protect his downside, but also allows him to profit from a risein bond prices if his expectation about increasing rates is incorrect.The disadvantage of this position isthat there is a price to pay for this protection – the option premium. Upside potential is unlimited butis reduced by the extent of the premium.

Profit/Loss

Long put

Long put hedgeLong portfolio

price

Optionpremium

Profit/Loss

Futures hedge

Long portfolio

price

Short futures

Profit/LossUnhedged position

Futures hedge

Long put hedgeprice

Short call hedge

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Sell callsIf the fund manager believed that rates where only likely to rise a small amount he could considerselling calls. In this situation we can see that the resultant position allows the fund manager to be inprofit should rates rise or fall within a certain range. However, the disadvantage is that if rates rise orfall by the extent of the premium taken in from the call sale, then the fund will have a capped upsideand an unprotected downside.

Clearly each alternative has its merits and it is up to the fund manager to decide which the mostappropriate strategy is.

Calculating the hedge ratioShould he elect to hedge his portfolio with either futures or options an appropriate hedge ratio wouldneed to be calculated. If the bonds in the portfolio were non deliverable then the modified durationapproach would be applied. In this situation the Basis Point Value (BPV) of the portfolio (ie the BPV ofa bond may be calculated as the dirty price of the bond multiplied by modified duration, then dividedby 100) is found and hedged using the BPV of a futures contract.The appropriate calculationsare shown below.

BPV of futures contract = BPV of CTD/Price factor of the CTD

The full hedge ratio is given as:

or

xBPV of CTD

BPV of portfoliox Price factor of CTD

nominal value of futures contract nominal value of portfolio

No. of futures =

BPV of future

BPV of portfoliox

nominal value of futures contract nominal value of portfolio

No. of futures contracts =

Profit/Loss

Short call Option premium

Long portfolio

price

Short callhedge

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ExamplePortfolio nominal value £100,000,000BPV of portfolio 8.81Futures nominal value £100,000BPV of futures CTD 8.82CTD price factor 1.1439664Price of CTD Bond 124.31Futures Price 108.18

= 1,143 contracts

Using futures in asset allocationA fund manager wishes to alter the duration of his portfolio. By buying futures he can increase theportfolio’s duration so that an expected fall in yields will present the fund manager with a greaterexposure to price increase sensitivity. In order to facilitate this process quickly, cheaply and withreduced execution risk he elects to use Euronext.liffe’s Block Trading Facility (explained later).

Calculation of portfolio duration

Duration adjustment with futuresIn order to adjust the duration (BPV) of the portfolio, the manager seeks to increase his portfolioBPV from 6.531 to 6.884.The following formula may be applied:

Initial risk = par amount x BPVi = 4,000m x 6.531

Target risk = par amount x BPVd = 4,000m x 6.884

Futures risk = par amount x (BPVd – BPVi) = 4,000m x (6.884 – 6.531)

Where:

BPVi is initial BPV of portfolio

BPVd is desired BPV of portfolio

BPVCTD = 6.56

CTDPF = 1.073288

1.14396648.828.81

£100,000£100,000,000

No. of futures xx=

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Par Par Accrued Market Modified Basis Yield Amount Price Interest Value Duration Point

Value

Long Gilt 6.77 2,500m 106.11 4.306 2760.4m 5.920 6.537

Long Gilt 6.68 1,500m 108.10 6.000 1711.5m 5.715 6.521

Total – 4,000m – – 4471.9m – –

Weighted average – – – – – 5.842 6.531

To calculate the number of futures required to increase the duration:

No. of futures =

=

=

= 2,310 contracts

Using Euronext.liffe’s Block Trading Facility the fund manager can efficiently adjust his position, avoidslippage and make considerable savings when compared with the transaction charges and risks he mayexperience if he chose to execute the trade in the underlying cash market.

The same principle can be applied if a fund manager holds a mixed currency portfolio and wishes toswitch from one asset class to another. For example, if the fund manager wished to reduce his Bundholding and increase his Long Gilt position, by using the same technique as described above, the fundmanager would simply sell an appropriate number of Bund futures and buy the corresponding numberof Long Gilt futures to the desired level. Conducting such a switch in the cash market can be costlyand precarious.An advantage of using futures is that the existing portfolio remains intact until a timewhen the fund manager feels it is appropriate to physically unwind his cash position when marketconditions prove favourable.

The Futures ‘Roll’When a futures contract is bought or sold, it is not always with the intention of holding the contractuntil expiry and then making or taking delivery of the underlying bond.A considerable proportionof the market use bond futures as a way of managing the (interest rate) risk of holding a bond.Thefutures contract will track the price of the underlying bond until it expires.As a futures contract nearsexpiry, the open interest (number of open positions) in the contract begins to decline as positions aretransferred into the next available contract.This is known as the ‘roll’.

112.6531.6884.6

1004000 −

xkm

PFCTD

id

CTDBPV

BPVBPVx

NotionalPar

/

−

futures

increase

BPV

BPVx

NotionalPar

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LIFFE CONNECT®

Euronext.liffe’s futures and options can be traded either through the central markets or by usingWholesale Trading Facilities, developed in recognition of the fact that markets need to provideguaranteed execution to support specific trading strategies.

LIFFE CONNECT® is Euronext.liffe’s electronic trading platform and is widely recognised as one ofthe most advanced derivatives trading platform in the world. It has a unique, flexible design that canaccommodate significant order flow and the transaction volumes associated with highly liquid, largevolume contracts.The combination of an open system design and high performance capacity makesLIFFE CONNECT® a uniquely powerful and flexible alternative to any existing electronic or floorbased trading platform.

LIFFE CONNECT® utilises an open system architecture that allows access via modern standard PCs,enabling a true customisation of front-end trading software. LIFFE CONNECT® has been designed totake advantage of recent advances in software, networking and hardware infrastructure, with a viewto facilitating access from any financial centre or indeed from any PC, around in the world.

To participate in the market, access is available on a subscription basis.To facilitate this process,Euronext.liffe has, and will continue to establish a series of strategic international hubs, which offer theopportunity for even more international users to participate directly in the market. Users accessingthe market will require a Trading Application, which links to the Euronext.liffe host via the LIFFECONNECT® Application Program Interface (API).These Trading Applications may be free standing orintegrated into a subscriber’s existing front/back office trading, settlement, risk management and orderrouting systems.

Access to LIFFE CONNECT®

To gain direct access to LIFFE CONNECT®, your firm can either do so as an exchange member or asan affiliate of an existing Euronext.liffe member.

LIFFE CONNECT® can be accessed electronically from the world’s major financial centres.Traderswishing to access LIFFE CONNECT® can do so via one of the many front-end trading applicationswhich have been developed by Independent Software Vendors (ISVs).These applications arepersonalised trading screens that link the user to the LIFFE market via a chosen network.

Customers have considerable flexibility and choice of network via which to access the market, including:

l direct access from London via the LIFFE market’s local Exchange Access System (EASy) network l direct access via Euronext.liffe’s international network provider l access through services offered by Value Added Network (VANs) partners l access via a member’s own network

Non-members of the LIFFE market may also access the market remotely via a number of indirectmethods which include:

l an order routing service offered to customers by a Euronext.liffe member, allowing a customer toenter his orders electronically to the member who, in turn, channels the order immediately ontoLIFFE CONNECT®

l trading bureaux, which allow independent traders to trade directly on LIFFE CONNECT® underthe umbrella of a Euronext.liffe member

l a broker with access to the LIFFE market

Accessing futures and options on the Euronext.liffe Market

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Trading on LIFFE CONNECT®

Trading on LIFFE CONNECT® is characterised by two important aspects, the anonymity of the marketand the trade priority matching algorithm. Other key characteristics of LIFFE CONNECT® include itsstrategy markets and implied pricing functionality.

Anonymity – Trading anonymity is a key aspect of the LIFFE CONNECT® market.Traders in themarket will not be aware of whose orders they are viewing or trading against, in the central orderbook, either before or after a trade.

Trade priority matching algorithm – Trading takes place through the submission of orders, usingthe member’s trading application, into the LIFFE CONNECT® central order book. Orders may be forindividual contract months, individual option series, or strategies. Once an order has been submitted,the system then matches orders in the central order book.The criteria for determining trade priority(ie which orders will trade first against each other) is dependent on the contract being traded.TheTrading Host configuration allows the trade matching algorithm to be set on a product by productbasis.The criteria used for this configuration will be one of the following:

l price and time priorityl price and pro-rata

Trading AlgorithmAll of Euronext.liffe’s Bond futures use the price/time trading algorithm whereas the Bond optionsuse the price and pro-rata trading algorithm.The price/time trading algorithm has the followingcharacteristics:

Price: highest bid/lowest offer has priority over orders in the same contract month/strategy

Time: the first order at a price has priority over all other orders at the same price which will,in turn, trade according to the time they were accepted by the Trading Host

The price and pro-rata trading algorithm has the following characteristics:

Price: highest bid/lowest offer has priority over other orders in the same contract month/strategy

Pro-rata: all orders at a price have the same priority; orders are filled in proportion to their volume

The pro-rata algorithm contains many variations. For Bond options it is Priority Order witha Minimum Volume Requirement and Volume Cap

The pro-rata algorithm can be adjusted on a product by product basis so that a specific degree ofpriority is given to the price maker before pro-rata sharing is applied in respect of any remainingbusiness. For each side of the market it allows one order in the book to be assigned a priority “flag”.Once a new incoming order has traded against the priority “flagged” order, the pro-rata algorithm willoperate in the normal way.The aim of this mechanism is to encourage market participants to improveprices by offering a reward of guaranteed volume, through the priority flagging of orders, in return forthe price improvement.

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An order will gain priority status if it betters the current best price in the order book. Only one orderin a particular market can have priority status, and as a result priority status is removed from anyprevious order. In order to gain this priority, the order must satisfy a minimum volume requirement.In addition, priority for this order will be limited by the imposition of a volume cap.

There will not always be a priority order in the order book.This can occur when the priority order isfully traded, leaving the other orders at the same or at a worse price, or when no orders which exceedthe minimum volume requirement have been submitted.

The minimum volume thresholdThe minimum volume requirement level is configurable by contract. If the first order at a new bestprice has a volume at or above the minimum volume threshold, then it will gain priority status. If thefirst order does not meet the minimum volume threshold (thus not gaining priority), no subsequentorders joining at that price will gain priority either, even if they meet the minimum volume threshold.The following example illustrates the minimum volume threshold:

The Long Gilt option has a minimum volume threshold of 50 lots.

The first order submitted to sell 50 lots at the best price (Order A) would gain priority status.A subsequent sell order of any size at the same best price (Order B) would not be given tradepriority. If a buy order for 60 lots at that price was then submitted to the Trading Host, OrderA would be given priority in execution and would be fully traded. Order B would receive theremaining 10 lots from the incoming buy order.

Where an order satisfying the priority requirements is subsequently bettered by an order submittedat an improved price, it will regain its priority once the better order has been executed or withdrawn,providing that the volume of that better order was below the minimum volume threshold. If thevolume of the order at the better price was at or above the minimum volume threshold then theoriginal order would lose its priority amongst other orders at that price and would be subject to thesimple pro-rata algorithm.

The maximum volume capAn order satisfying the priority requirements described above will also be subject to a volume capwhich will limit the trading priority of the order up to a maximum level. Once the “priority” volumehas traded, any remaining volume will be treated on a prorate basis along with all other orders at thatprice.The following example illustrates the maximum volume cap:

The Long Gilt option has a minimum volume threshold of 50 lots and a volume cap of 500 lots.

A new order to sell 520 lots at a new best price (Order C) will gain trading priority since it satisfiesthe minimum volume threshold.A second order submitted to sell 40 lots (Order D) at the same pricewill join the offer but not gain any priority status.

29

If a buy order for 200 lots at that price was submitted, 200 lots of Order C would be executedimmediately. Priority for a further 300 lots (ie up to the maximum volume cap of 500 lots, includingthe 200 lots already executed) would be retained by order C. If a buy order for 330 lots at that priceis submitted, 300 lots of the remainder of Order C would be executed immediately. However, theremaining 20 lots of Order C and the 40 lots of Order D would be executed on a pro-rata basisagainst the remaining 30 lots of the buy order, with Order D receiving 20 lots and Order C receivinga further 10 lots.

For Long Gilt options, the minimum volume requirement is currently 50 lots and the maximumvolume cap is 500 lots.

If you would like further information on LIFFE CONNECT®, please see www.euronext.com or emailliffeconnect@liffe.com.

Wholesale Trading FacilitiesEuronext.liffe provides three wholesale trading facilities that recognise the need to provide certainty ofexecution to support defined trading strategies and are designed to complement the central market.

These Wholesale trading facilities comprise:

l Block Tradingl Basis Tradingl Asset Allocation

Of the three wholesale facilities available, Block Trading and Basis Trading are applicable to Bondfutures and options. In providing these facilities, Euronext.liffe meets the markets’ needs whilst strikingthe right balance between the central market and the certainty of execution.

Euronext.liffe’s Block Trading FacilityThe Block Trading Facility allows Euronext.liffe members and their Wholesale Clients (see definitionbelow) to transact business of significant size as bilaterally agreed transactions on-Exchange, withoutdelay and with certainty of price and execution.

Block Trades are subject to minimum threshold levels. Euronext.liffe members may not aggregateseparate orders to meet minimum threshold requirements. Euronext.liffe will monitor and adjust,when necessary, the minimum size threshold of Block Trades to protect the quality of marketon LIFFE CONNECT®. Please refer to Euronext.liffe’s website (www.euronext.com) for currentthreshold levels.

Contracts eligible for transaction via the Block Trading FacilityAll bond futures and option contracts listed by the Exchange are eligible for trading via this facility.Block traded contracts become positions indistinguishable from positions created through electronictrading (thus making Block Trades subject to the standard contractual and clearing structures ofthe market).

30

Available to members and wholesale clients onlyThere are no restrictions on Euronext.liffe members themselves entering into Block Trades. However,with respect to non-members of Euronext.liffe, only “Wholesale Clients” (ie those with sufficientknowledge, expertise and understanding of the implications of the facility) will be able to participate inBlock Trades.

Before a Euronext.liffe non-member client may participate in the facility, the Euronext.liffe membermust satisfy himself that the client meets these criteria.The client must also be notified in writing, inadvance, that he is to be treated as a Wholesale Client for the purposes of Block Trading. In addition,before any given Block Trade may take place, the member will be required to make it clear to his client(whether the client is a Euronext.liffe member or not) that the quote he is being given is a Block Tradeprice and not a “market price” (ie prevailing LIFFE CONNECT® price).

PricingBlock Trades may legitimately take place at prices different to the prevailing market price. However,Euronext.liffe has determined that members must ensure that any Block Trade price quoted satisfiesfair market value principles ie that such a price is fair and reasonable given the lot size of the BlockTrade and the price and size of business being quoted in the central market.As an additional safeguard,the Exchange and LCH.Clearnet will require members to justify any trades negotiated at apparentlyabnormal levels and will reserve the right to refuse to register any such trades.

Registration and reporting of Block tradesEuronext.liffe members have 3 minutes, from the verbal agreement of the details of a Block Tradebetween the parties concerned, in which to report the Block Trade to the Exchange.

Block Trades will be included within existing price reports, albeit with a separate trade type indicator“K”. It is possible that Block Trades create new highs/lows, as is already the case for volatility andstrategy trades.Therefore market participants are advised to ensure that they review and amend(as appropriate) any arrangements they may have with their clients regarding the execution of anyorders which depend upon specific trading levels being reached (eg “stop” orders).

Euronext.liffe’s basis trading facilityEuronext.liffe’s Basis Trading Facility – the BTF – permits market users to enter into a conditionaltransaction in a Euronext.liffe futures contract and a corresponding cash instrument.

What is a basis trade?A basis trade is the simultaneous exchange of a financial asset or instrument (eg a cash bond, OTCswap, or a basket of stocks) together with an appropriate offsetting number of futures contracts, ina privately negotiated transaction between two parties.

The cash leg is not traded on Euronext.liffe, but is traded in the normal way between the twocounterparties, with the requirement that the member provides, if requested, evidence of the cashleg transaction.

31

BTF trading proceduresExchange members may organise basis trades outside the central order book and present the requiredtrade details to Exchange for authorisation. Once validated, the volume and the contract traded arepublished to the market as a whole, and Euronext.liffe staff register the trade on behalf of the member.

Any Exchange member with the requisite trading right for the contract in question can arrange abasis trade. If not, trade details can be provided to the Exchange via a member who has.The memberpresenting the trade to the Exchange is referred to as the basis trade executing member.

Basis trades can be transacted during normal trading hours of the contract concerned. Registrationslips must be presented to the Exchange within 30 minutes of the trade being arranged, and no laterthan 15 minutes before the close of trading in the Euronext.liffe contract. Basis trades may bearranged on any trading day up to the day before the first notice day of the delivery month.

Registration and reporting of basis tradesThe executing member must assign the price to the futures leg of the trade.This price must be withinthe high/low range for the contract in question during the 30 minutes before the trade is submitted.If there has not been a trade in the last 30 minutes, the price assigned must be within theoreticalhigh/low range calculated by the Exchange for the same period. Basis trades are not allowed in afutures delivery month that has never traded.

Summary reference information on the cash leg of the basis trade should be provided to the Exchangeon the registration slip presented at the time of transaction. However, full details of this cash leg trademust be retained by the executing member, including evidence of trade completion, and be madeavailable to the Exchange on request.

Euronext.liffe specifies what is acceptable for the cash leg of the trade, and on the ratio between theamount of cash and futures traded.

The following instruments can be used as the cash leg of a basis trade:

l Government Bonds l Non-Government Bondsl Vanilla interest rate swapsl Forward Rate Agreementsl “Repo” Transactionsl OTC Options

Details of the futures leg will be distributed to Quote Vendors, marked with the trade typeindicator “J”. Further information regarding Euronext.liffe’s BTF facility can be obtained fromwww.euronext.com

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Margining is the deposit of cash or collateral with the clearing house when you create a futures oroptions position.

The role of the clearing houseThe margining system is one of the unique distinctions of exchange traded futures as opposed tothe operation of over-the-counter (OTC) markets for derivative products.The margining systemprovides important protection to the market. Central to this protection is the clearing house.Euronext.liffe’s clearing house, LCH.Clearnet, guarantees trades registered by LCH.Clearnet members.Any Euronext.liffe member who is not a member of LCH.Clearnet must therefore have a clearingagreement with a member of LCH.Clearnet (ie a clearing member) in order to transact business onthe Exchange.There are several categories of clearing member at Euronext.liffe, all of whom aresubject to minimum financial requirements laid down by Euronext.liffe and LCH.Clearnet.

LCH.Clearnet members clearing Euronext.liffe business fall into one of three categoriesof membership:

l a general clearing member (GCM) is entitled to clear Euronext.liffe transactions made for itsown account and for its clients, and for the accounts of non clearing members under the termsof a standard clearing agreement;

l an individual clearing member – public order (ICM POM) is entitled to clear trades executedfor its own account and its clients only; and

l an individual clearing member – non public order (ICM NPOM) is entitled to clear tradesexecuted for its own account only.

Having satisfied LCH.Clearnet’s criteria and gained membership of one of the three clearing categoriesreferred to above, LCH.Clearnet members are monitored by LCH.Clearnet to ensure that theycontinue to meet specified criteria.

Once LCH.Clearnet has registered a trade, it becomes the central counterparty to the buyingand selling clearing members, by a legal process known as novation.As central counterparty,LCH.Clearnet ensures the financial performance of trades through to delivery.To assess and controlthe risk associated with its position as central counterparty, LCH.Clearnet has a comprehensiverisk management approach. Central to this is the calculation and collection of initial and variationmargin payments.

Variation marginThe day to day gains and losses of all participants are collected by clearing member firms andpresented to LCH.Clearnet. Continuous accounting and collection ensures that all members’customers receive the gains (and pay the losses) associated with their positions each day.Thiscontinuous collection and payment programme insulates members’ customers from the potentialof losing access to their gains earned during the course of substantial market movements overextended periods of time.

At the same time the process offers its members a signal for the early identification of customerswho might be unable to fulfil their obligations.The members’ first line of protection comes fromthe collection of daily variation margin, the mechanism for day-to-day collection of gains and losses.This protection is augmented by the collection of initial or ‘SPAN®’ margin, which provides protectionto LCH.Clearnet against the default of a clearing member.

Margining

33

One of the largest and most significant differences between ‘forward’ markets and futures markets isthe handling of day-to-day gains and losses. Generally in over-the-counter forward markets, all of thegains or losses associated with a position are exchanged at some designated date in the future.Thisdeferral or disassociation between the economic event causing a gain or loss and its ultimate paymentintroduces a level of credit risk.The counterparties must each consider if the other will be capable ofpaying what might become a very substantial sum at some deferred date. Such a practice introduces ahigh degree of ‘credit’ risk between counterparties leading to the requirement that firms investigateeach other’s financial conditions and set credit lines and limits for each potential counterparty.An enormous investment in credit screening results from this practice.

On Euronext.liffe, the process of members’ daily collection and payment of variation margin effectivelyremoves a vast amount of this credit risk from customers’ concerns.A customer who had purchasedfutures and then watched the market move up from the purchase price will have received the profitsof the position on a daily basis and need not be concerned with the ability of any specific counterpartyto be able to pay their losses at a distant future date.

The determination of the daily settlement priceThe key to the variation margin process is the Exchange’s determination of an accurate dailysettlement price for each and every futures and options contract.At the close of trading of a contract,the Exchange publishes a final end of day price. If at the close there is insufficient trading volume toobserve this final price the Exchange officials will use the price generated by the Exchange pricingmodel, pertinent to the futures or options contract, which is based on prices from the underlyingmarket. Settlement prices are automatically transmitted to member back offices.

Options – delayed payment of premiumThe same variation margin calculation applies to options on futures. For these options the premiumis not paid in-full up front, but takes the form of variation margin payments and receipts.

Initial marginThe initial margin provides protection to the member and LCH.Clearnet in the event that sufficientclient funds are not readily available to satisfy day to day variation margin requirements. In this way theinitial margin acts as a deposit which may be used by the member to satisfy the customer’s or clearingmember’s obligations if the customer or clearing member fails to do so.The amount of this initialmargin is set by LCH.Clearnet based on historical trends in terms of market price volatility as wellas forthcoming events which may further affect volatility.

SPAN® margining requirementsThe initial margining system employed by LCH.Clearnet is SPAN® (Standard Portfolio Analysis ofRisk) which was originally developed by the Chicago Mercantile Exchange.The SPAN® system looks atboth futures and options contracts relating to a single underlying contract/portfolio (such as all Giltfutures and options positions, across a range of different contract months). It then defines a range ofpotential movements of futures prices (both up and down), called a ‘scanning range’, and a range ofpotential changes in the implied volatility of options, called a ‘volatility shift’.An account’s initial marginrequirement is calculated as the largest possible loss that a customer’s portfolio (including all futuresand options positions based on the same underlying instrument) would face in the worst case scenarioof market events.

34

This largest possible loss is known technically as ‘scanning risk’. Futures contracts’ values are notaffected by the movements in implied volatility of options and thus the largest possible loss willcome from the greatest futures market movement.The determination of a ‘scanning range’ byLCH.Clearnet, effectively defines the initial margin requirement for a position involving a single futurescontract.These scanning ranges are periodically reviewed by LCH.Clearnet and can be adjusted ascircumstances change. Scanning ranges are not changed with great frequency and can be relied uponwithout requirement to consult LCH.Clearnet on a daily basis. Frequent checks however are made.

Euronext.liffe rules concerning initial margins, stipulate that clients must be charged at least the samelevel as LCH.Clearnet would charge clearing members in respect of the same position.

The scanning risk is not the entire amount of initial margin required.A position’s initial marginrequirement will also reflect charges and credits associated with all of the other contracts maintainedin the customer’s account. Some of these are explained briefly below.

Inter-month spread chargeIn the case of a customer with a position including both long positions for delivery in one contractmonth and short positions in the same bond futures contract for a different delivery month, asubstantially reduced margin will be levied.The SPAN® system imposes an inter-month spread chargereflecting possible changes in the basis which is significantly lower than it would be if the long andshort legs were calculated individually.

Spot month chargeBetween the last trading day and the delivery day, a ‘spot month’ charge is added to the calculationof the initial margin requirement to cover the risk of a delivery default on delivery during thedelivery process.

Inter-commodity creditThe SPAN® system recognises that there are strong correlation’s between some contracts traded onEuronext.liffe and credits accounts with offsetting positions in these correlated contracts (eg longLong Gilts versus short Bunds).

Levels of protection and supervisionMembers of the Exchange are supervised at several levels.The Exchange itself is responsible forenforcing rules relating to fair trading practices and the ongoing behaviour of its own members andtheir employees in their handling of customer orders and accounts. Customers may be concerned asto the level of protection and supervision offered in the safekeeping of their initial margin deposits.The Financial Services Authority (FSA) is a self regulatory organisation operating under the FinancialServices Act 1986.The FSA has responsibility for creating policies relating to its members’ conduct,overseeing members’ activities and enforcing its policies.

Due to the fact that brokers are required to collect initial margins from customers and to enforce therules of LCH.Clearnet as regards maintenance of sufficient margins in customer accounts, the FSA hasestablished rules and procedures governing the members’ handling of those funds.The cornerstone ofcustomer protection is the principle of ‘segregation’. Customer funds held in fulfilment of margin rulesand requirements must be kept separate from, or segregated from, the member firms’ own funds.Audit teams from the FSA make regular, unannounced visits to member firms to confirm compliancewith rules covering the segregation and integrity of customer funds.

Further information on SPAN® margining can be found on www.euronext.com.

35

4. Price Factor4.01 The List of Deliverable Gilts published by the Board in respect of a delivery month under

term 3.01 will specify a price factor (the “Price Factor”) for each Deliverable Gilt calculatedin accordance with:

(a) in the case of a Deliverable Gilt which is fully paid, the formula set out in term 4.02; and(b) in the case of a Deliverable Gilt which is not fully paid, the formula published from time to

time by General Notice.

4.02 (a) For each Deliverable Gilt which is fully paid the Price Factor will be calculated in accordancewith the formula:

P(6)100

where P(6) equals the price per £100 nominal of such Deliverable Gilt at which it has a grossredemption yield of 6% per annum, calculated as at the first day of the delivery month, minusthe undiscounted amount of accrued interest on such Deliverable Gilt on that day, using theformulae set out in paragraphs (b) and (c) of this term.

(b) P(6) shall be calculated in accordance with the following formula:

where: d1 = Cash flow (which could be zero) due on the following quasi-coupon date, per £100nominal of the gilt. d1 will be zero if the first day of the delivery month occurs in the ex-dividend period or if the gilt has a long first coupon period and the first day of thedelivery month occurs in the first full coupon period. d1 will be less than c/2 if the firstday of the delivery month falls in a short first coupon period. d1 will be greater than c/2if the first day of the delivery month falls in a long first coupon period and the first dayof the delivery month occurs in the second full coupon period;

d2 = Cash flow due on the next but one quasi-coupon date, per £100 nominal of the gilt. d2

will be greater than c/2 if the first day of the delivery month falls in a long first couponperiod and in the first full coupon period . In all other cases,d2 = c/2;

c = Annual coupon per £100 nominal of the gilt;

r = Number of calendar days from and including the first day of the delivery month up tobut excluding the next quasi-coupon date;

s = Number of calendar days in the full coupon period in which the first day of the deliverymonth occurs;

n = Number of full coupon periods between the following quasi-coupon date and theredemption date;

AI = Accrued interest per £100 nominal of the gilt calculated using the formula set out in (c);

AI-1.03

100+

1.03

1-

1.031

06.0c

03.11.03

1=P(6)

nn2

1

++

dd

s

r

36

Appendix ALong Gilt futures contract price factor

(c) The accrued interest (AI) in the formula set out in paragraph (b) will be calculated inaccordance with the following formulae:

(i) If the first day of the delivery month occurs in a standard coupon period, and:

the first day of the delivery month occurs on or before the ex-dividend date:

the first day of the delivery month occurs after the ex-dividend date:

where: AI = Accrued Interest per £100 nominal of the gilt;

c = Annual coupon per £100 nominal of the gilt;

t = Number of calendar days from and including the last coupon date up to but excludingthe first day of the delivery month;

s = Number of calendar days in the full coupon period in which the first day of the deliverymonth occurs;

(ii) If the first day of the delivery month occurs in a short first coupon period, and:

the first day of the delivery month occurs on or before the ex-dividend date:

the first day of the delivery month occurs after the ex-dividend date:

where: t* = Number of calendar days from and including the issue date up to but excluding the firstday of the delivery month;

r = Number of calendar days from and including the issue date up to but excluding the nextquasi-coupon date;

and c and s have the same meanings as in (i) above.

(iii) If the first day of the delivery month occurs in a long first coupon period, and:

the first day of the delivery month occurs during the first full coupon period:

2su

=AI1

c×

2st

=AI* cr ×−

2s=AI

* ct ×

21

st

=AIc×

−

2st

=AIc×

37

the first day of the delivery month occurs during the second full coupon period and on orbefore the ex-dividend date:

the first day of the delivery month occurs during the second full coupon period and afterthe ex-dividend date:

where: u = Number of calendar days from and including the issue date up to but excluding the firstday of the delivery month;

s1 = Number of calendar days in the full coupon period in which the issue date occurs;

s2 = Number of calendar days in the next full coupon period after the full coupon period inwhich the issue date occurs;

r1 = Number of calendar days from and including the issue date up to but excluding the nextquasi-coupon date;

r2 = Number of calendar days from and including the quasi-coupon date after the issue dateup to but excluding the first day of the delivery month which falls in the next fullcoupon period after the full coupon period in which the issue date occurs;

and c has the same meaning as in (i) above.

Short and long first coupon periodsWhen the DMO issues Gilts, it tries to arrange the payment of coupons on a standard cycle.Currently it is every March and September. However the auctions themselves do not always occur oncoupon dates.This means that a Gilt which is auctioned on a date which is between standard couponpayment dates will have a long or short first coupon.The PF formulae above illustrates the differentmethods by which accrued interest must be calculated depending on whether the first coupon periodis standard, long, or short.

21

s

r=AI

2

2 c×

−

2sr

=AI2

2

1

1 csr ×

+

38

Bond futures

Long Gilt JGB

ADP LN# NJ#

Bloomberg Financial Markets G A <CMDTY> N A <CMDTY>

Bridge Profit Centre GB\R GB\N

Bridge Station GB@R GB@N

CQG QG QJ

Futuresource LGL LJB

Reuters FLG:<F3> FYB:<F3>

Telerate 25693 25603

ILX Global Systems TOPIC3 20012 20021

Track Data LG’ LJ’

Bond options

Long Gilt

ADP FG#

Bloomberg Financial Markets G A <CMDTY> OMON

Bridge Profit Centre GB\R

Bridge Station GB@R

CQG QG

Futuresource PLGL/CLGL

Reuters FLG++<F3>

Telerate 25605-25620

ILX Global Systems TOPIC3 19900

Track Data LG’

Appendix BQuote vendor contract codes

39

Introductory to IntermediateIntroduction to Derivatives Don ChanceISBN 0-03003-588-0 Dryden

Options and Financial Futures David DubofskiISBN 0-07112-583-3 McGraw Hill

Introduction to Futures and Options Markets John HullISBN 0-13783-317-2 Prentice Hall

Futures Options and Swaps Robert KolbISBN 1-57718-063-1 Blackwell

Options as a Strategic Investment Lawrence G. McMillanISBN 0-13636-002-5 New York Institute of Finance

Option Volatility and Pricing Sheldon NatenbergISBN 1-55738-486-X McGraw Hill

Intermediate to AdvancedFixed Income Mathematics Frank FabozziAnalytical and Statistical Techniques IrwinISBN 0-78631-121-5

Valuation of Fixed Income Securities Frank Fabozziand Derivatives FJFISBN 1-88324-906-6

Option Futures and other Derivatives John HullISBN 0-13264-367-7 Prentice Hall

The European Bond Basis Christopher PlonaISBN 0-7863-0852-4 Irwin

Money Market and Bond Calculations Stigum and RobinsonISBN 1-55623-476-7 Irwin

Dynamic Hedging N.TalebManaging Vanilla and Exotic Options WileyISBN 0-471-15280-3

40

Appendix CFurther reading

Amsterdam P.O. Box 19163,1000 GD Amsterdam,The Netherlands.Tel: +31 (0)20 550 5555 Fax: +31 (0)20 550 4900

Brussels Palais de la Bourse/Beurspaleis,Place de la Bourse/Beursplein,1000 Brussels,Belgium.Tel: +32 (0)2 509 12 11 Fax: +32 (0)2 509 12 12

LisbonAv. da Liberdade, no° 196, 7° Piso,1250-147 Lisbon,Portugal.Tel: +351 21 790 00 00Fax: +351 21 795 20 26

LondonCannon Bridge House,1 Cousin Lane,London EC4R 3XX,United Kingdom.Tel: +44 (0)20 7623 0444Fax: +44 (0)20 7588 3624

Paris 39, rue Cambon,75039 Paris Cedex 01,France.Tel: +33 (0)1 49 27 10 00Fax: +33 (0)1 49 27 11 71

www.euronext.com

June 20064434/June-06/500/US