Interest Rate Swaps
Introduction
Consider the following term structure of interest rates
Years to Maturity
1
2
3
Yield Rate
4.5%
5%
6%
The implied (forward) annual rates are (check it!)
Year 1
Year 2
Year 3
4.500000%
5.502392%
8.028662%
We want to find a fixed annual rate
R
% for all three years that will be equivalent to the implied
annual rates above. We first turn the annual rates to money amounts by considering interest earned
on $100 for each year (paid at the end of each year):
Year 1
Year 2
Year 3
Interest by Implied Rate
4.500000
5.502392
8.028662
Interest by Fixed Rate
R
R
R
0
1
2
3
4.500...
5.502...
8.028...
R
R
R
The two cashflows should have the same present values at
t
= 0 (by the term structure), so
4
.
500000
1
.
045
+
5
.
502392
1
.
05
2
+
8
.
028662
1
.
06
3
=
R
1
.
045
+
R
1
.
05
2
+
R
1
.
06
3
(solving) =
⇒
R
= 5
.
932146. Therefore, the fixed rate is 5.932146%. This is the
swap rate
.
Exercise
With the same term structure as above, you want to enter an interest rate swap such that the rate
for the first year is 0%, and the rates for the second and the third year are both
Y
%. Find
Y
.
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 Spring '12
 yuy
 Pk, Interest, Interest Rate, Yield Curve, Interest rate swap

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