1、Chapter 6Interest Rate FuturesOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20191Day Count ConventionDefines:the period of time to which the interest rate appliesThe period of time used to calculate accrued interest (relevant when the instrument is bought of soldOption
2、s, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20192Day Count Conventions in the U.S. (Page 129)Treasury Bonds:Actual/Actual (in period)Corporate Bonds:30/360Money Market Instruments:Actual/360Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20193E
3、xamplesBond: 8% Actual/ Actual in period. 4% is earned between coupon payment dates. Accruals on an Actual basis. When coupons are paid on March 1 and Sept 1, how much interest is earned between March 1 and April 1?Bond: 8% 30/360Assumes 30 days per month and 360 days per year. When coupons are paid
4、 on March 1 and Sept 1, how much interest is earned between March 1 and April 1?Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20194Examples continuedT-Bill: 8% Actual/360:8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period b
5、y 360. How much interest is earned between March 1 and April 1?Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20195The February Effect (Business Snapshot 6.1)How many days of interest are earned between February 28, 2019 and March 1, 2019 whenday count is Actual/Actual
6、in period?day count is 30/360?Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20196Treasury Bill Prices in the USOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20197price quoted is $100 per price cash is 100360PYYnP)(Treasury Bond Price Quot
7、esin the U.S Cash price = Quoted price + Accrued InterestOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20198Treasury Bond FuturesPages 132-136 Cash price received by party with short position = Most recent settlement price Conversion factor + Accrued interestOptions, F
8、utures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20199ExampleMost recent settlement price = 90.00Conversion factor of bond delivered = 1.3800Accrued interest on bond =3.00Price received for bond is 1.380090.00+3.00 = $127.20 per $100 of principalOptions, Futures, and Other Derivati
9、ves, 8th Edition, Copyright John C. Hull 201910Conversion Factor The conversion factor for a bond is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. H
10、ull 201911CBOT T-Bonds & T-NotesFactors that affect the futures price:Delivery can be made any time during the delivery monthAny of a range of eligible bonds can be deliveredThe wild card playOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201912Eurodollar Futures (Page
11、136-141)A Eurodollar is a dollar deposited in a bank outside the United States Eurodollar futures are futures on the 3-month Eurodollar deposit rate (same as 3-month LIBOR rate)One contract is on the rate earned on $1 millionA change of one basis point or 0.01 in a Eurodollar futures quote correspon
12、ds to a contract price change of $25 Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201913Eurodollar Futures continuedA Eurodollar futures contract is settled in cashWhen it expires (on the third Wednesday of the delivery month) the final settlement price is 100 minus t
13、he actual three month Eurodollar deposit rateOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201914ExampleOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201915DateQuoteNov 1 97.12Nov 297.23Nov 396.98.Dec 2197.42ExampleSuppose you buy (take a
14、 long position in) a contract on November 1The contract expires on December 21The prices are as shownHow much do you gain or lose a) on the first day, b) on the second day, c) over the whole time until expiration?Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201916Exam
15、ple continuedIf on Nov. 1 you know that you will have $1 million to invest on for three months on Dec 21, the contract locks in a rate of 100 - 97.12 = 2.88%In the example you earn 100 97.42 = 2.58% on $1 million for three months (=$6,450) and make a gain day by day on the futures contract of 30$25
16、=$750 Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201917Formula for Contract Value (page 137)Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201918If Q is the quoted price of a Eurodollar futures contract, the value of one contract is 10,
17、000100-0.25(100-Q)This corresponds to the $25 per basis point ruleForward Rates and Eurodollar Futures (Page 139-141)Eurodollar futures contracts last as long as 10 yearsFor Eurodollar futures lasting beyond two years we cannot assume that the forward rate equals the futures rateOptions, Futures, an
18、d Other Derivatives, 8th Edition, Copyright John C. Hull 201919There are Two ReasonsFutures is settled daily whereas forward is settled onceFutures is settled at the beginning of the underlying three-month period; FRA is settled at the end of the underlying three- month period Options, Futures, and
19、Other Derivatives, 8th Edition, Copyright John C. Hull 201920Forward Rates and Eurodollar Futures continued A “convexity adjustment” often made isForward Rate = Futures Rate0.5s2T1T2 T1 is the start of period covered by the forward/futures rateT2 is the end of period covered by the forward/futures r
20、ate (90 days later that T1)s is the standard deviation of the change in the short rate per year(often assumed to be about 1.2%Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201921Convexity Adjustment when s s=0.012 (page 141)Options, Futures, and Other Derivatives, 8th
21、Edition, Copyright John C. Hull 201922Maturity of Futures (yrs)Convexity Adjustment (bps)23.2412.2627.0847.51073.8Extending the LIBOR Zero CurveLIBOR deposit rates define the LIBOR zero curve out to one yearEurodollar futures can be used to determine forward rates and the forward rates can then be u
22、sed to bootstrap the zero curveOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201923Example (page 141-142)so thatIf the 400-day LIBOR zero rate has been calculated as 4.80% and the forward rate for the period between 400 and 491 days is 5.30 the 491 day rate is 4.893% O
23、ptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201924121122TTTRTRF211122)(TTRTTFRDuration MatchingThis involves hedging against interest rate risk by matching the durations of assets and liabilitiesIt provides protection against small parallel shifts in the zero curveOpt
24、ions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201925Use of Eurodollar FuturesOne contract locks in an interest rate on $1 million for a future 3-month period How many contracts are necessary to lock in an interest rate on $1 million for a future six-month period?Options,
25、Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201926Duration-Based Hedge RatioFFPDVPDVFContract price for interest rate futuresDFDuration of asset underlying futures at maturityPValue of portfolio being hedgedDPDuration of portfolio at hedge maturityOptions, Futures, and Other
26、Derivatives, 8th Edition, Copyright John C. Hull 201927Example It is August. A fund manager has $10 million invested in a portfolio of government bonds with a duration of 6.80 years and wants to hedge against interest rate moves between August and DecemberThe manager decides to use December T-bond f
27、utures. The futures price is 93-02 or 93.0625 and the duration of the cheapest to deliver bond is 9.2 yearsThe number of contracts that should be shorted isOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2019287920. 980. 650.062,93000,000,10Limitations of Duration-Based
28、HedgingAssumes that only parallel shift in yield curve take placeAssumes that yield curve changes are smallWhen T-Bond futures is used assumes there will be no change in the cheapest-to-deliver bondOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201929GAP Management (Bus
29、iness Snapshot 6.3)This is a more sophisticated approach used by banks to hedge interest rate. It involvesBucketing the zero curve Hedging exposure to situation where rates corresponding to one bucket change and all other rates stay the same Options, Futures, and Other Derivatives, 8th Edition, Copy
30、right John C. Hull 201930Liquidity RiskIf a bank funds long term assets with short term liabilities such as commercial paper, it can use FRAs, futures, and swaps to hedge its interest rate exposureBut it still has a liquidity exposure. It may find it impossible to roll over the commercial paper if the market loses confidence in the bankNorthern Rock is an exampleOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201931谢谢你的阅读v知识就是财富v丰富你的人生
