Problem Set 8:
ACTSC 231 Mathematics of Finance, Fall 2010
Q1.
A callable bond with a face value of $1,000 has 8% semiannual coupons and is redeemed
at par. The possible range for the early redemption is at the end of the 10th through
the 15th years at par. Find the price of this callable bond if the yield is guaranteed to
be at least
(a) 6% convertible semiannually, and
(b) 10% convertible semiannually.
Q2.
A $1,000 bond with semiannual coupons with rate 4% per year matures at the end of 10
years. The bond is callable at $1,050 at the ends of years 4 through 6, at $1,025 at the
ends of years 7 through 9, and at $1,000 at the end of year 10. Find the maximum price
that an investor is willing to pay to obtain a (guaranteed) yield rate of 5% convertible
semiannually.
Q3.
You are given the following prices of $1,000 par value bonds with 10% annual coupons:
$1,028.04 for 1 year term, $1,036.53 for 2 years term, $1034.47 for 3 years term Find
the spot rates
r
t
for
t
= 1
,
2
,
3 that are implied by these bond prices.
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 Fall '09
 Chisholm
 Finance, yield rate

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