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Chapter Fourteen
Swap Pricing
Answers to Problems and Questions
1. If the options are
European style
you can use the put/call parity model with
C – P = 0, meaning K = S (1+R)
T
.
Here we have K = 28.55 x (1.055)
0.5
=
29.32
If the options are
American style,
a naïve but convenient way to solve this is by
using trial and error with the CBOE options calculator.
We have the following
input variables:
S = $28.55
T = six months
R = 5.50%
σ = any value; it doesn’t matter.
Assume 25%.
We find that with a striking price of
29.35
the put premium and the call
premium are identical to the nearest penny.
2. The swap
price
is the fixed interest rate one party to the swap pays.
The swap
value
is the present value of the payments one party makes to the other.
The
swap can have positive value to one party and negative value to the other.
3. If the swap is atthemarket this means that the swap price is the rate that
causes the swap to have zero present value to the parties to the swap.
4. The payoff diagram for a short swap slopes down and to the right like the
diagram for a short stock position.
You can view this as the simultaneous
holding of a short call and a long put, or a short cap and a long floor.
5. The new Libor rates would be
Spot (
0
f
3
)
5.77%
Six Month (
0
f
6
)
5.85%
Nine Month (
0
f
9
)
5.92%
Twelve Month (
0
f
12
)
5.97%
50
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View Full DocumentChapter Fourteen.
Swap Pricing
Solve for the 3 x 6 forward rate:
2
4
0585
.
1
4
1
4
0577
.
1
+
=
+
+
f
3
f
6
=
5.93%
Solve for the 6 x 9 forward rate:
3
2
4
0592
.
1
4
1
4
0585
.
1
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 Spring '10
 n/a
 Pricing

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