tutorial4sol - TUTORIAL 4 WEEK 5 ECON3107/ECON5106...

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TUTORIAL 4– WEEK 5 ECON3107/ECON5106 – Economics of Finance ANSWERS 1. (i) The Q matrix derived from the elemental payment combinations B0, S0, Bg, Sg, Bb, Sb is as follows: Q = 1 . 1 1 . 5 - 1 - 1 0 0 1 . 1 0 . 8 0 0 - 1 - 1 0 0 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 0 0 0 0 0 0 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 The corresponding securities price vector is p S = ( 1 1 0 0 0 0 ) . (ii) The Q matrix derived from the elemental payment combinations B0, S0, Bb, Sb, B02, S02 is as follows: Q = 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 - 1 - 1 0 0 0 0 0 0 1 . 21 2 . 25 0 0 0 0 1 . 21 1 . 20 0 0 1 . 1 1 . 5 1 . 21 1 . 20 0 0 1 . 1 0 . 8 1 . 21 0 . 64 The corresponding securities price vector is p S = ( 1 1 0 0 1 1 ) . (iii) The atomic security price vector can be derived from either Q matrix and its corresponding p S vector: p atom = p S · Q - 1 = ( 0 . 389 61 0 . 519 48 0 . 151 80 0 . 202 40 0 . 202 40 0 . 269 86 ) (iv) Using the elemental payment combinations from part (i) we get: n = Q - 1 c = 1 . 1 1 . 5 - 1 - 1 0 0 1 . 1 0 . 8 0 0 - 1 - 1 0 0 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 0 0 0 0 0 0 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 - 1 0 10 20 20 30 40 = 63 . 839 - 34 . 694 18 . 182 0 46 . 753 - 14 . 286 Using the elemental payment combinations from part (ii) we get: n = Q - 1 c = 1 . 1 1 . 5 0 0 0 0 1 . 1 0 . 8 - 1 - 1 0 0 0 0 0 0 1 . 21 2 . 25 0 0 0 0 1 . 21 1 . 20 0 0 1 . 1 1 . 5 1 . 21 1 . 20 0 0 1 . 1 0 . 8 1 . 21 0 . 64 - 1 0 10 20 20 30 40 = 47 . 310 - 34 . 694 28 . 571 - 14 . 286 16 . 529 0 1
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