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Unformatted text preview: ACTSC 445: AssetLiability Management Department of Statistics and Actuarial Science, University of Waterloo Solutions for Unit 8 Exercises 1. Figure 1 shows the value of the bond obtained at the different nodes of the lattice. The price at time 0 is 70.84. The corresponding spot rate is (100 / 70 . 84) . 25 1 = 0 . 09. 84.13 87.88 90.83 93.12 78.56 70.84 71.63 75.54 81.37 86.00 Figure 1: Finding P (0 , 4) 2. Using spot rates, we get 10 1 1 . 06 + 1 1 . 07 2 + 1 1 . 08 3 + 110 1 1 . 09 4 = 104 . 033 . 3. We get V (1 , 1) = 102 . 4387, V (1 , 0) = 103 . 4039 and V (0 , 0) = 107 . 1703. 4. (i) At time 1, in node (1,1) we sell 124 . 69 84 . 155 units of the zerocoupon bond with maturity at t = 3, and each unit has a value of 0.816608. We thus get $33.10. We add 105 . 32 69 . 583 × 1 . 06 = 31 . 562 in the bank account, so the net cashflow is 1.54, as desired. In node (1,0), we buy 84 . 155 74 . 486 units of the zerocoupon bond, each unit being worth 0.866354, for a total amount of $8.377, and withdrawof the zerocoupon bond, each unit being worth 0....
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This note was uploaded on 10/24/2010 for the course ACTSC 445 taught by Professor Christianelemieux during the Fall '09 term at Waterloo.
 Fall '09
 ChristianeLemieux

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