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Consider the discount factors for the following eight dates
Date
3m
6m
9m
1y
15m
18m
21m
2y
Price
0.9928
0.9849
0.9762
0.9689
0.9580
0.9495
0.9407
0.9325
a) What is the forward price today for delivering at date t2 = 6m a zcb with face value $100,000 maturing at t4 = 1y?
b) What is the price of a bond paying semi-annual coupon at the rate of 6.50% maturing in 21 months? Report both the clean and the dirty price. (You can assume here that each month is 30 days.)
What is the forward price for delivering the bond at t2 = 6m (per $100 face value)? [Also report the dirty price.]
c) Suppose that you have such a forward position (acquired earlier) with a delivery price of K = $103.25 for $3.1M face value. What is the value of your forward position?
d) What is the dollar duration of this position? This quantity captures, to the first order, the dollar change induced by the entire yield curve shifting down by 1.
[Think of all the cash flows the forward position confers until the maturity of the bond, t7 = 21m. The forward position is a "portfolio" of all these cashflows.]
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