Problem 1
|
Mat. Date
|
Rate(%)
|
|
1/15/2017
|
0.5
|
|
4/15/2017
|
0.6
|
|
7/15/2017
|
0.75
|
|
10/15/2017
|
1.0
|
|
1/15/2018
|
1.25
|
|
4/15/2018
|
1.5
|
|
7/15/2018
|
1.75
|
|
10/15/2018
|
2.0
|
|
1/15/2019
|
2.1
|
|
4/15/2019
|
2.2
|
|
7/15/2019
|
2.3
|
|
10/15/2019
|
2.4
|
Table 1: Continuously compounded zero rate
As of 10/15/2016, Table 1 gives continuously compounded zero rates for the corresponding quarterly maturity dates. Using this data:
a) Derive the present value factors as of 10/15/2016 for these dates.
b) As of 10/15/2016 (trade date), derive the corresponding fixed rate on a 3-year interest rate swap where fixed is exchanged for floating. Assume that both the fixed and floating payments are made twice a year. Assume that there is no difference between trade date and effective date, and that the payments fall on the corresponding semi-annual maturity dates with no adjustment for holidays. Finally, assume that the rates are paid on a 30/360 basis.
c) Using the same information as in b), show all the payments on the three-year interest rate swap where you pay the annual three-year fixed swap rate and receive the 6-month floating rate. List expected payments at the forward rates when the floating payments are not known on the trade date. Assume a notional of $50 Million on the swap.