
Explanation:
A 1 basis point shift in the 0-1 year forward rates shifts the yield for the first year, and its impact spreads over all cash flows occurring during and after this period because they must all be discounted through the first year. Calculating the present values of cash flows discounted at 2% per period (4% semiannual rate): For a 0-1 year forward bucket, a 1 bp increase in forward rates reduces the present value of all cash flows proportional to their exposure to the 0-1 year bucket, giving a cumulative DV01 impact of approximately 0.0099. For the 1-2 year forward bucket, only the cash flows occurring in the 1-2 year period (at 1.5 and 2.0 years) are discounted by the shifted forward rates. The DV01 for this bucket is approximately 0.0094. Therefore, the 0-1 year forward bucket 01 is 0.0099, and the 1-2 year forward bucket 01 is 0.0094.
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Q.54 Suppose that two-year with USD 100 of face value pays a coupon of 5% when there are two buckets: 0-1 year and 1-2 years. Suppose further that the term structure is flat at 4% with semiannual compounding. What are the forward bucket 01s?
A
0-1 year forward bucket 01 is 0.0099; 1-2 year forward bucket 01 is 0.0094.
B
0-1 year forward bucket 01 is 0.00965; 1-2 year forward bucket 01 is 0.00965.
C
0-1 year forward bucket 01 is 0.0004; 1-2 year forward bucket 01 is 0.0189.
D
0-1 year forward bucket 01 is 0.0094; 1-2 year forward bucket 01 is 0.0099.