ACTSC 445/845 – Solutions – Midterm 2
1. [10 points] Consider the following binomial tree,
where
q
(
t, n
) = 0
.
6
for all nodes
(
t, n
), and
one period is equal to one year.
1
2
0
5%
3.8%
5.5%
4.5%
5.2%
6.4%
Based on this tree, determine the price a callable bond with face value 100, coupon rate of 6%
per year, and maturity at time 2. The bond can be called at time 1 and at time 2 (but not at
time 0). When called at time 1, the issuer must pay a redemption value of $102 rather than $100.
At time 2, the redemption value is $100.
Solution:
We have
V
(1
,
1)
=
min(102
,
106
/
1
.
055) = 100
.
47
V
(1
,
0)
=
min(102
,
106
/
1
.
038) = 102
V
(0
,
0)
=
1
1
.
05
(0
.
6(100
.
47 + 6) + 0
.
4(102 + 6)) = 101
.
98
.
It was also possible to compute the price of the optionfree bond and then subtract the value of
the call option.
2. [10 points] Consider the following binomial tree, where
q
(
t, n
) = 0
.
5 for all nodes (
t, n
), and one
period is equal to one year.
1
2
0
4%
4.2%
4.5%
5%
6%
?
(a) Given that a zerocoupon bond with face value 100 and maturity at time 2 has a price of
92.01, determine
i
(1
,
1).
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 Fall '09
 ChristianeLemieux
 Telus

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