Explanation:
We have 92 days (=30+30+31+1 in March, April, May, and June respectively) between March 1 and June 1 and 184 days (=30+30+31+30+31+31+1 in March, April, May, June, July, August, and September, respectively).
We know that,
Dirty price = Quoted price + Accrued interest
= $120 + \frac{92}{184} \times 3 = 121.50$
There are no coupon payments for the 30-day period between June 1 and July 1.
The dirty futures price is therefore:
$121.50 \times e^{\frac{30}{365} \times 0.05} = 122.00$
We have 123 days (=30+31+31+1 in June, July, August, and September, respectively) between June 1 and Sep 1.
The accrued interest on July 1 is, therefore:
$3 \times \frac{123}{184} = 0.6685$
The clean futures price is, therefore: $122.00 - 0.6685 = 121.3315$
Thus, the futures price can be estimated by:
Q.4924 Suppose that the bond that will be cheapest to deliver in a Treasury bond futures contract pays annual coupons of 6% per annum on March 1 and September 1 and will be delivered on July 1. Suppose further that the bond's quoted price on June 1 is 120.00, and its conversion factor is 1.2424. If all interest rates are 5% continuously compounded, what is the estimated futures price on July 1?
A
98.78
B
120.00
C
97.66
D
122.00
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