Fin 448: FixedIncome Securities
Homework Solution 1
Wei Yang
1
Bootstrapping
(1.1) ... (1.4)
We solve the following equations by the iterative procedure
98
.
16 =
p
0
.
5
100
99
.
50 =
p
0
.
5
3
.
5
2
+
p
1
(100 +
3
.
5
2
)
103
.
31 =
p
0
.
5
6
.
625
2
+
p
1
6
.
625
2
+
p
1
.
5
(100 +
6
.
625
2
)
99
.
63 =
p
0
.
5
4
.
25
2
+
p
1
4
.
25
2
+
p
1
.
5
4
.
25
2
+
p
2
(100 +
4
.
25
2
)
which yield
p
0
.
5
= 0
.
9816
,
p
1
= 0
.
9610
,
p
1
.
5
= 0
.
9377
,
p
2
= 0
.
9156
and translate to
y
0
.
5
= 3
.
75%
,
y
1
= 4
.
02%
,
y
1
.
5
= 4
.
34%
,
y
2
= 4
.
46%
(1.5)
The annualized, semiannually compounded yield for the 2year Treasury
is found by solving
99
.
63 =
4
.
25
2
1 +
y
2
1
+
4
.
25
2
1 +
y
2
2
+
4
.
25
2
1 +
y
2
3
+
100 +
4
.
25
2
1 +
y
2
4
which yields
y
= 4
.
45%
(1.6)
The par coupon rate is determined from
1 =
p
0
.
5
c
2
+
p
1
c
2
+
p
1
.
5
c
2
+
. . .
+
p
n
1 +
c
2
to be
c
= 4
.
44%
1
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(1.7)
If we switch to continuous compounding, the yields are computed from the
prices by
p
k
=
e

y
k
k
and so
y
0
.
5
= 3
.
71%
,
y
1
= 3
.
98%
,
y
1
.
5
= 4
.
29%
,
y
2
= 4
.
41%
2
Arbitrage
(2.1)
Using the zerocoupon bond prices, the price of X is
p
0
.
5
3
2
+
p
1
3
2
+
p
1
.
5
3
2
+
p
2
(100 +
3
2
) = 97
.
26
(2.2)
The calculated price falls within the bid ask spread of the market quotes.
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 Spring '10
 WeiYang
 4.34%, 4.02%, 4.41%, 4.29%

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