A Note On Interest Rate Futures
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QUOTED FUTURES PRICE Contd..The logical step to calculate the quoted futures price is shown in Table III. TABLE III
STEPS TO CALCULATE QUOTED FUTURES PRICE
Step 1: Calculate the cash price of the cheapest-to-deliver
bond from the quoted price.
Step 2: Calculate the cash futures price from the cash bond
price using the above equation.
Step 3: Calculate the quoted futures price from the cash futures
price.
Step 4: Divide the quoted futures price by the conversion
factor. |
Source: Hull C. John, “Options, Futures and Other Derivatives”
Example:
Assume that in a T-bond futures contract, the cheapest to deliver bond
is a 14% coupon bond with a conversion factor of 1.37. Delivery will
take place after 280 days. The term structure is flat and the rate of
interest is 10% per annum. Assume that the current quoted bond price is
$120 with semi-annual coupons. The last coupon date was 45 days ago, the
next coupon date will be 137 days from the present date, and the next to
next coupon date will be in 320 days from the present.
The diagrammatic representation would be: |
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Given the current quoted bond price of $120, the cash price would be the
quoted price plus the accrued interest,
= 120 + [45/(45+137) X 7] = $121.73
The present value of the coupon payment of $7 to be received after 137 days
(0.3753 year) is,
= 7e-0.3753 X 0.1 = 6.742
The futures contract last for 280 days (= 0.7671 year). The cash futures
price of a 14% bond would therefore be:
(121.73 – 6.742)e 0.7671 X 0.1 = 124.155
At the point of delivery, the accrued interest would be for 143 days. This
has to be deducted from the cash futures price to calculate the quoted
futures price,
124.155 – 7 X [143/(143+40)] = 118.685
The contract is written on a standard 6% bond, and 1.37 standard bonds are
considered to be equivalent to each 14% bond. Therefore, the quoted futures
price would be,
118.685/1.37 = 86.63
CONCLUSION
EXHIBIT I LIST OF ACTIVELY TRADED SHORT TERM INTEREST RATE FUTURES
EXHIBIT II LIST OF ACTIVELY TRADED LONG TERM INTEREST RATE FUTURES
EXHIBIT III T-BILL FUTURES AND EURODOLLAR FUTURES
EXHIBIT IV NO ARBITRAGE FUTURES PRICE
EXHIBIT V CHARACTERISTICS OF T-NOTE AND T-BONDS
EXHIBIT VI CHEAPEST TO DELIVER BOND
ADDITIONAL READINGS & REFERENCES
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