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MidtermTwo_Summer2009

# MidtermTwo_Summer2009 - ACTSC 445/845 – Solutions –...

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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 option-free 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 zero-coupon bond with face value 100 and maturity at time 2 has a price of 92.01, determine i (1 , 1).

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MidtermTwo_Summer2009 - ACTSC 445/845 – Solutions –...

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