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Assignment 2Answers

Assignment 2Answers - Comm 374 Assignment#4 Question1 a...

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Comm 374 Assignment #4 Question1 a) Using the course formula gives F=S(1+R)= 40*1.04 = $41.60 b) Hedging a long forward position is going to be less costly due to dividend. Using the duplication argument (see the table in Slide 13) it can be shown that F=(S –PV(D)) (1+R)= (40 -2/1.04^0.75)*1.04= $39.58. Another method will lead to the same conclusion is to assume that XYZ delivered a dividend of FV(D)=2*1.04^0.25 at the end of year in which case the formula of slide 13 is directly applicable: F=40*.104 - 2*1.04^0.25=$39.58. c) F = 45*(1.04)^0.5=$45.89. Question2: a. It is easy to check that R2=4%, R3=4.5% and R1=4.26% b. We construct a cash and carry strategy whereby we short the forward, we buy Bond 3 and borrow its price (98.68), we get the no arbitrage price F=98.67*1.0426 – 4 =98.67 Question3. a. First you calculate the stock tree: 48.4 44 40 39.6 36 32.4 The option payoff at the end (last three nodes) are 0 2.4 9.6 Then using the method in the course, you can easily derive the delta/B to calculate by backward induction the price in each node. The result is B 12.80988 delta -0.27273 0 0.80988 1 Delta -0.4936 2.1184 8 2.4 1
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B 21.8626 4 4.75871 2 delta -1 9.6 B 40.75871
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