Hull經(jīng)典衍生品教科書第9版官方PPT,第6章

1、Chapter 6Interest Rate FuturesOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20141Day 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, 9th Edition, Copyright John C. Hull 20142Day Count Conventions in the U.S. (Page 132)Treasury Bonds:Actual/Actual (in period)Corporate Bonds:30/360Money Market Instruments:Actual/360Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20143E

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, 9th Edition, Copyright John C. Hull 20144Examples 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, 9th Edition, Copyright John C. Hull 20145The February Effect (Business Snapshot 6.1)How many days of interest are earned between February 28, 2015 and March 1, 2015 whenday count is Actual/Actual

6、in period?day count is 30/360?Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20146Treasury Bill Prices in the USOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20147price 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, 9th Edition, Copyright John C. Hull 20148Treasury Bond FuturesPages 135-140 Cash price received by party with short position = Most recent settlement price Conversion factor + Accrued interestOptions, F

8、utures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20149ExampleMost 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, 9th Edition, Copyright John C. Hull 201410Conversion 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, 9th Edition, Copyright John C. H

10、ull 201411CBOT 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, 9th Edition, Copyright John C. Hull 201412Eurodollar Futures (Page

11、140-145)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, 9th Edition, Copyright John C. Hull 201413Eurodollar 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, 9th Edition, Copyright John C. Hull 201414ExampleOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201415DateQuoteNov 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, 9th Edition, Copyright John C. Hull 201416Exam

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, 9th Edition, Copyright John C. Hull 201417Formula for Contract Value (equation 6.2, page 141)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201418If Q is the quoted price of a Eurodollar futures contract, the value of one c

17、ontract is 10,000100-0.25(100-Q)This corresponds to the $25 per basis point ruleForward Rates and Eurodollar Futures (Page 143-145)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 rateOption

18、s, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201419There 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,

19、 Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201420Forward 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 for

20、ward/futures rate (90 days later that T1)s is the standard deviation of the change in the short rate per yearOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201421Convexity Adjustment when s s=0.012 (page 144)Options, Futures, and Other Derivatives, 9th Edition, Copyrigh

21、t John C. Hull 201422Maturity 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 used to bootstrap

22、the zero curveOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201423Example (page 144-145)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% Options, Futures,

23、and Other Derivatives, 9th Edition, Copyright John C. Hull 201424121122TTTRTRF211122)(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 curveOptions, Futures, an

24、d Other Derivatives, 9th Edition, Copyright John C. Hull 201425Use 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, Futures, and Othe

25、r Derivatives, 9th Edition, Copyright John C. Hull 201426Duration-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 Derivatives, 9th

26、Edition, Copyright John C. Hull 201427Example 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 futures. The futur

27、es price is 93-02 or 93.0625 and the duration of the cheapest to deliver bond will be 9.2 years at the futures contract maturityThe number of contracts that should be shorted isOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014287920. 980. 650.062,93000,000,10Limitations of Duration-Based 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 ch