Problem set #3 Solution

Problem set #3 Solution - Problem Set 3 Solutions Econ 136,...

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1 Problem Set 3 Solutions Econ 136, Fall 2009 A note about grading: 5: no major or minor errors 4: no more than a few minor errors 3: a major or many minor errors 2: multiple major errors 1: multiple major errors and portions left blank 0: blank or never turned in. 1. Dynamic Trading a) As before, we price using LOOP by 1) calculating the payoff of the asset, 2) constructing a replicating portfolio, 3) pricing the asset using the price of the replicating portfolio. - Calculate the payoff. S is the state-contingent payoff and equals the number of heads, and X = 0.2, so using the formula for the call payoff we get State S Put payoff: max (S-X, 0) 2 Heads 2 max (2-0.2, 0) = 1.8 1 Head 1 max (1-0.2, 0) = 0.8 0 Heads 0 max (0-0.2, 0) = 0 - Create a replicating portfolio. From lecture, we know (first four columns): State AD1 AD2 AD3 Call Option 1.8*AD1 + 0.8AD2 + 0*AD3 2 Heads 1 0 0 1.8 1.8 1 Head 0 1 0 0.8 0.8 0 Heads 0 0 1 0 0 Price 0.25 0.50 0.25 ? 1.8*0.25 + 0.8*0.5 = 0.85 We can replicate the payoff of the call option by constructing a portfolio of 1.8 shares of AD1 and 0.8 shares of AD2. - Price the call using LOOP. The price of the replicating portfolio is 1.8*0.25 + 0.8*0.5 = 0.85. This is the price at date zero for buying the call option. b) To construct a dynamic trading strategy directly for the put option, we need to work backwards on the event tree. There are three time periods: t=0, 1, 2.
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Problem set #3 Solution - Problem Set 3 Solutions Econ 136,...

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