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Interest rate futures

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

DAY COUNT AND QUOTATION CONVENTIONS TREASURY BOND FUTURESEURODOLLAR FUTURESDuration-Based Hedging Strategies Using FuturesHEDGING PORTFOLIOS OF ASSETS AND LIABILITIES

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

The interest earned between the two dates

Day Count Conventions in the U.S.

Treasury Bonds:Actual/Actual (in period) Corporate and municipal Bonds:30/360Money Market Instruments:Actual/360

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Bond Principal 100Coupon Payment dates 3/1 , 9/1(reference period)Coupon Rate 8%Calculate the interest earned between 3/1 and 7/3 Treasury bond Actual/Actual (in period)

Corporate and municipal Bonds 30/360

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

*Day counts can be deceptive(business snapshot)

2/28 2005, 3/1 2005

Which would you prefer?Treasury bond or Corporate and municipal Bonds

Answer: Corporate and municipal Bonds 30/360

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

P is the quoted price(discount rate)Y is the cash pricen is the remaining life of the Treasury bill measured in calendar days

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Face Value = 100Quoted Price = 8Interest over the 91-day life=2.0222

Interest Rate for the 91 day period=2.064%

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Treasury Bond Price in the U.S are quoted in dollars and thirty-second of a dollarThe quoted price is for a bond with a face value of $100Cash price = Quoted price +Accrued Interest

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

2010/3/52010/1/102010/7/10Face Value = 100Coupon Rate = 11%Quoted Price = 95-16 or $95.502018/7/10Accrued Interest=Cash price= $95.5+$1.64=$97.14The cash price of a $100000 bond is $97140

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Treasury bond future price are quoted in the same way as the Treasury bond prices themselves.One contract involves the delivery of $100000 face value of the bondA $1 change in the quoted futures price would lead to a $1000 change in the value of the future contractDelivery can take place at any time during the delivery month

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Cash prices received by party with short position=(Most Recent Settlement Price Conversion factor) + Accrued interestExample Settlement price of bond delivered = 90.00 Conversion factor = 1.3800 Accrued interest on bond =3.00 Price received for bond is (1.380090.00)+3.00 = $127.20per $100 of principal

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

The party with the short position receives = (Most recent settlement price Conversion factor)+ Accrued interestThe cost of purchasing a bond = Quoted bond price + Accrued interestThe cheapest-to-deliver is Min [Quoted bond price (Most recent settlement price Conversion factor)]

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

The most recent settlement price =93-08, 93.25

The cost of delivering each of the bonds:Bond1:99.59 (93.25 1.0382)= $2.69Bond2:143.50 (93.25 1.5188)=$1.87Bond3:119.75 (93.25 1.2615)=$2.12 Quoted bond price (Most recent settlement price Conversion factor)]

BondQuoted bond price($)Conversionfactor199.591.03822143.501.51883119.751.2615

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

A number of factors determine the cheapest-to-deliver bond [Quoted bond price (Most recent settlement price Conversion factor)] Bond Yields 6%

Yield Curve is

The Wild Card Play

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

An exact theoretical future price for the treasury bond contract is difficult to determineAssume both the cheapest-to-delivery bond and the delivery date are known

F: future priceS: spot price I : present value of the coupons during the life of future contract

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Cheapest-to-deliver coupon rate 12%Conversion factor 1.4000Current quoted bond price $120Interest rate 10% annumDelivery will take place in 270 daysCoupon paymentCoupon paymentCoupon paymentCurrent timeMaturity of futures contract60 days122days148days35daysCash priceThe present value of a coupon of$6 will be received after 122 days (0.3342years)

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Coupon paymentCoupon paymentCoupon paymentCurrent timeMaturity of futures contract60 days122days148days35daysThe futures contract lasts for 270 days (0.7397years)The cash price, If the contract were written on the 12%

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Coupon paymentCoupon paymentCoupon paymentCurrent timeMaturity of futures contract60 days122days148days35daysThere are 148 days of accrued interest. The quoted futures price, if the contract were written on the 12% bond, is calculated by subtracting the accrued interestThe quoted future price =

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

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 million

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Eurodollar futures contracts last as long as 10 yearsWhen it expires (on the third Wednesday of the delivery month) the final settlement price is 100 minus the actual three month deposit rate 100-R

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

If Q is the quoted price of a Eurodollar futures contract, the value of one contract is 10,000[100-0.25(100-Q)]A change of one basis point or 0.01 in a Eurodollar futures quote corresponds to a contract price change of $25 The $25 per basis point rule is consistent that an interest rate per year changes by 1 basis point, the interest earned on 1 million dollar for 3 months change by 10000000.0001(0.01%) 0.25(3)=25 or $25

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

For Eurodollar futures lasting beyond two years we cannot assume that the forward rate equals the futures rateThere are Two Reasons reduce the forward rate1.Futures is settled daily where forward is settled once2.Futures is settled at the beginning of the underlying three-month period; forward is settled at the end of the underlying three- month period

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Consider the situation where =0.012 and we wish to calculate the forward rate when the 8-year Eurodollar futures price quote is 94. 1. In this case T1=8, T2=8.25, and convexity adjustment is or 0.475%(47.5 basis points)

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

2.The future rate is 6% per annum on an actual/360 basis, annual rate of 6%(365/360) = 6.083%

3.The estimate of the forward rate is 6.083-0.475=5.608%

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Maturity of FuturesConvexity Adjustment (bps)23.2412.2627.0847.51073.8

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

LIBOR deposit rates define the LIBOR zero curve out to one yearOnce the convexity adjustment just described has been made, Eurodollar futures are often used to extend the zero curve Eurodollar futures can be used to determine forward rates and the forward rates can then be used to extend the zero curveIt is usually assumed that the forward interest rate calculated from the future contract applies to the

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Suppose that Fi is the forward rate calculate from the ith Eurodollar futures contract and is the zero rate for a maturity Ti

equation(4.5) So that

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

If the 400 day LIBOR rate has been calculated as 4.80% with continuous compounding and the forward rate for the period between 400 and 491 days is 5.30%, the 491 days rate is 4.893%

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Define:

FCContract price for interest rate futuresDFDuration of asset underlying futures at maturityPValue of portfolio being hedgedDPDuration of portfolio at hedge maturity

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

Assumes that only parallel shift in yield curve take placeAssumes that yield curve changes are smallIt is approximately true that (4.15) It is also approximately true The number of contracts required to hedge against an uncertain is

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

When the hedge instrument is a Treasury bond futures contract , the hedger must base on an assumption that one particular bond will be delivered, this mind the hedger must estimate the cheapest-to-deliver bond the interest rates and future prices move in opposite direction

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

It is August 2. 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 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 is

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

This involves hedging against interest rate risk by matching the durations of assets and liabilitiesIt provides protection against small parallel shifts in the zero curveDuration matching does not immunize a portfolio against nonparallel shifts in the zero curve

Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005

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 6th Edition, Copyright John C. Hull 2005

*ures*************

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