# Answers_to_ECON3107_assessment_1[1] - Name Susan Bai...

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Name: Susan Bai Student number: z3252854 Class: Friday, 9-10 Question 1: Mat lab Operations >> Q= [20 60 45; 20 30 5; 20 5 0] >> ps= [18 19 8] >> P_atom= ps*inv (Q) >>P_atom = 0.15 0.25 0.50 >>P_atom * [80 50 25]’ = 37PA (Value of the Apple Tree) i) The figure 0.15 refers to the arbitrage free price of the atomic security in good weather where 0.15 present apples in the first period can be traded for 1 good weather apple in the second period. 0.25 refers to the arbitrage free price of the atomic security when in the fair weather state where 0.25 present apples in the first period can be traded for 1 fair weather apple in the second period. And 0.50 is the arbitrage free price of the atomic security when it is in the bad weather state, where 0.50 present apples in the first period can be traded for 1 bad weather apple in the second period. ii) >>P_atom * [80 50 25]’ = 37PA (Value of the Apple Tree) >> The arbitrage free price of an apple tree is 37PA. iii) From the summation of the atomic security prices, the discount factor works out to be 0.9. The discount factor tells us the present value cost (payment) required to obtain one unit of apple in the second period, no matter what the state of the world is. iv) The first way to complete the market is by including security C in the Q payoff matrix, by doing so the investor needs to invest 2.7353 PA in the bond, short sell 0.9412 PA in the stock and invest 0.7059PA in security C to achieve

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