Solutions to Extra Problems 4c

Solutions to Extra Problems 4c - ACTSC 231 Solutions for...

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Unformatted text preview: ACTSC 231 Solutions for Problem Set 4 c 1. Fr = 5000 & : 10 2 = 250 , The bond can be replicated by taking 2.5 units & 250 100 = 2 : 5 of the 26-week T-bill plus 52.5 units ( 5000+250 100 = 52 : 5) of the 52 week T-bill. Let X be the price of the 52 week T-bill. The cost of the replicated bond is 2 : 5 (98 : 5) + 52 : 5 X . By no arbitrage this must equal the price of the bond, or 2 : 5 (98 : 5) + 52 : 5 X = 5194 : 38 = ) X = 5194 : 38 & 2 : 5(98 : 5) 52 : 5 = 94 : 25 2.a) P = 20 1 + i (2) ;: 5 2 & 1 +520 1 + i (2) ; 1 2 & 2 = 20 & 1 + : 07 2 & 1 +520 & 1 + : 075 2 & 2 = 502 : 41 b) 502 : 41 = 20 1 + i (2) 2 & 1 + 520 1 + i (2) 2 & 2 = ) 520 v 2 j + 20 v j & 502 : 41 = 0 = ) v j = & 20 p (20) 2 & 4(520)( & 502 : 41) 2(520) = & 20+ p (20) 2 & 4(520)( & 502 : 41) 2(520) = 0 : 963 90 (need v j > 0) i (2) = 2 & 1 : 963 90 & 1 = 7 : 490 4% (you can also use the &nancial functions on your BA II) 3. a) P = Q + kFr = 20 (103 : 62) + & 28 181 80 = 2084...
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