Bond futures. Bond futures contracts are futures contracts that allow investor to buy in the

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1 Bond futures INRODUCION Bond futures contracts are futures contracts that allow nvestor to buy n the future a theoretcal government notonal bond at a gven prce at a specfc date n a gven quantty. Compared to other futures, bond futures are slghtly more complcated as the underlyng bond of the futures contract s not a physcal bond but rather a theoretcal notonal bond determned by the basket of avalable delverable government bonds ssued n the market. Bond futures are very lqud futures contracts and among the most traded futures contracts. he most common ones are: In the US markets: US reasury bond Futures, often referred to as Bond Future. In Europe: Bund Future (Germany, Euro denomnated), Glt Future (UK, Brtsh Pound denomnated), Notonel contract (France, Euro denomnated). Bond futures are wdely used to hedge nterest rate rsk on long maturtes, especally by swap dealers that needs to cover ther rsk aganst varous ponts of the nterest rate curve. Bond futures bear an addtonal rsk often referred to as the bass rsk compared to swaps. Before revewng the varous concepts of bond futures and ts complcated delvery mechansm, let us gve practcal detals for most common contracts.

2 CONRAC DEAILS able 1 gves the detals of the most common bond futures: -Bond, the Gld Future, the Bund Future 1 and the French notonel contract. Contract US -Bond Bund UK Glt Fr Notonel Delvery March (H), June (M), March (H), June (M), March (H), June (M), March (H), June (M), months September December (Z) (U), September December (Z) (U), September December (Z) (U), September December (Z) (U), Quotaton Percentage Percentage Percentage Percentage Contract Sze $100, , , ,000 Coupon 8% 6% 7% 3.5% ck Sze 1/32 =$ = = = 10 Last radng 7 workng days pror 2 busness day pror 2 busness day pror 2 busness day pror day to the last busness day n expry month to the delvery day to the delvery day to the delvery day Delvery day Any busness day n 10th calendar day of Any busness day n 3 rd Wednesday of delvery months the delvery month delvery months the delvery month (seller choce) or the next followng (seller choce) busness day Settlement Any US reasury Any Bund wth Any delverable Glt Any bond wth bond wth more that maturty between 8.5 wth maturty maturty between years Bond non to 10.5 years Mn. between 8.75 and to 10.5 years Mn. callable for 15 years outstandng amount 13 years outstandng amount of 4 bllon of 6 bllon Margn requrement $5000 ntal $4000 mantenance 2000 ntal 2000 ntal spread margn 250 able 1: characterstcs of common bond futures 1, he Bund futures s now the most lqud bond future world-wde

3 INVOICE PRICE AND CONVERSION FACOR Government bond futures are based on a notonal bond, whch s a theoretcal bond whose prce s nferred from market physcally avalable bonds. he potentally delverable bonds need to satsfy certan crtera (see table 1). Lke for any other bond, the nvoce prce of the bond future has to account for the accrued nterest on the delvered bond. Invoce prce = Invoce Prncpal Amount + Accrued nterest (1.1) he nvoce prncpal amount receved by the short has to account for the characterstc of the bond delvered. o adjust for these characterstcs, the short receves a total notonal amount equal to the standard notonal tmes the converson factor (CF). he dea behnd the converson factor s to make the varous bonds equal provded that the nterest rate curve was flat wth a gven yeld 2 (see converson factor) Invoce prncpal amount = Future prce * Future Notonal * CF (1.2) 2 he converson factor s computng the value of the bond for a flat yeld. In the case of the Bund futures contract, the converson factor assumes a 6% yeld whle t s 8% for the -Bond futures. For a C.... bond wth n coupon: ( ) pad at tme ( ) = 1 n 1 n CF = C 100 n + n = 1 + % ( 1+ 6% ) ( 1 6 ) converson factor should be greater than 1 and the opposte s also true. =, ths leads to. On can notce that f the coupons are hgher than 6%, the

4 CHEAPES O DELIVER In case of delvery, the short decdes whch bonds to delver among the lst of potental bonds. Obvously, she chooses the cheapest-to-delver, referred to as the CD. When delverng the bond : She receves the quoted futures prce F tmes the converson factor plus the accrued nterest AI : F * CF + AI CF She pays a total cost of delverng the bond gven by the drty prce of the bond, that s equal to the clean prce B plus the accrued nterest. AI he cheapest to delver bond s therefore the one that maxmses her proft: 0 = ArgMax ( F CF B ) Example: usng the example of the table 2 and that the Bund future prce s 109.2, we get that the bond would cost respectvely: 1.69 (= *109.2), 2.38, he cheapest to delver would therefore be the frst bond. Many parameters nfluence the cheapest to delver bond. When yelds are hgher than the assumed yeld for the converson factor (6% for the Bund futures and 8% for the -Bond future) the converson methodology ten to favour low coupon and long maturty bonds. Smlarly, when yelds are lower, cheapest to delver bonds are often hgh coupons, low maturtes. Also when

5 the yeld curve s upward slopng (respectvely downward slopng), longmaturtes (respectvely short-maturtes) bond are preferred. Lastly, some bonds trade at a premum because of partculartes that makes them attractve lke bonds whose coupon can be strpped easly from the bond. MODELLING OF HE SHOR S OPIONS More accurate modellng of the delvery of the bond s qute complcated. here are a varety of embedded optons that the short party holds. Frst, the short s long an opton to choose any bond wthn the delverable bond basket, referred to a swtch or qualty opton. he short may hedge the bond futures usng an assumed cheapest to delver (wth ts forward prce computed accurately) and a swtch opton to change from the assumed cheapest to delver to another bond. So even f she holds a specfc bond aganst delvery, t the curve shfts, she may decde to delver another cheaper bond. here s also a tmng opton when the bond hold for delvery pays a coupon hgher than the cost of fnancng of the spot poston (the repo rate). If the bond provdes a coupon hgher than the repo rate mpled to calculate the forward value of ths bond, the short would be better off delverng the bond as late as possble. When one uses Black Scholes to value these small detals, one fnds that ths s very neglgble at frst sght and can be gnored n most cases. WILD CARD PLAY AND END OF HE MONH OPION wo embedded optons hold by the short have receved more attenton, as there are the most mportant optons. he wld card play refers to the US =-

6 Bond futures. here s a tme delay of roughly 2-hour between the close of the CBO reasury bond futures market (at 2pm Chcago tme) and the tradng of reasury bond market (at 4pm Chcago tme). Furthermore, the short can wat untl 8 pm to ssue to the clearnghouse a notce of ntenton to delver. hs gves the short the optonalty, referred to the wld card play, to choose the best tmng to buy the bond at the cheapest prce. Lastly the end of the month opton refers to the fact that the short can wat untl the last day of the tradng month to decde whether to delver or not whle the last tradng day s 7 busness day pror to the end of the month for the -bond and 2 busness day for the Bund futures contract. Coupon Maturty Converson Quote Prce Cost Rate (%) Factor able 2: Example of delverable bonds. Prce of the Bund futures

7 Entry category: futures Scope: contract detals, notonal bond, Cheapest to delver, delvery opton, uses, cost of carry, model for bond futures, repo. Related artcles: repurchase agreement, bond valuaton. Erc Benhamou 3 Swaps Strategy, London, FICC, Goldman Sachs Internatonal 3 he vews and opnons expressed heren are the ones of the author s and do not necessarly reflect those of Goldman Sachs

8 References Hull, John C, Optons, Futures, and Other Dervatves, Fourth Edton, Prentce-Hall, 2000

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