Consider a Multi-period Binomial Model with T = 2, r = 1/3, S 0 =...
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Consider a Multi-period Binomial Model with T = 2, r = 1/3, S 0 = 2, d = 5/4, u = 3/2, and p = 3/5. Let X be a European put option with strike price $4.00 and expiration time 2. Let C0 denote the price of one share of the contingent claim at time zero, C u 1 = C1(1) = C1(2) denote the price of one share of the claim at time one on the event {1 = u} and C d 1 = C1(3) = C1(4) denote the price of one share of the claim at time one on the event {1 = d}. (a) Suppose that C u 1 = 1/16. Note: You do not know C0 or C d 1 , but that is not necessary. (i) Give an example of an arbitrage opportunity such that t {1, 0, 1} for t = 1, 2. (ii) Explain why the example that you provided is a trading strategy. (iii) Compute V0() = 0. (iv) Demonstrate that is self-financing. (v) Compute V2(). (vi) Use the above to argue that is an arbitrage opportunity. (b) Suppose that C u 1 = 1. Note: You do not know C0 or C d 1 , but that is not necessary. (i) Give an example of an arbitrage opportunity such that t {1, 0, 1} for t = 1, 2. (ii) Explain why the example that you provided is a trading strategy. (iii) Compute V0() = 0. (iv) Demonstrate that is self-financing. (v) Compute V2(). (vi) Use the above to argue that is an arbitrage opportunity
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