Problem Set 2
Problem 1 (20 points)
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.