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This is a Finance Options, Futures, and Derivatives assignment. I do not understand how to proceed because I can not figure out how to get

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This is a Finance Options, Futures, and Derivatives assignment. I do not understand how to proceed because I can not figure out how to get u and d to start the equations.

image text in transcribed
Problem 1. Consider a European call option on a non-dividend paying stock with an exercise price of $50 that expires in 3 months. The riskless interest rate (r) is 5%, the underlying asset is worth $50, and its volatility (a) is 20%. Assume continuous compounding; i.e., the one timestep discount factor is e'r'\". Also assume that: I 1 timestep; 6t 2 1 / 12 (i.e., there will be 3 monthly timesteps until expiration); and I The \"up\" move, it = cam, and the \"down\" move (I = e'o'm. This option can be dynamically replicated by purchasing A shares of the stock and borrow- ing B dollars at each of the nodes in the binomial tree. Use the dynamic replicating portfolio approach to nd the current price (p) of such a call option. (Hint: you will need to compute values for A, B, and c at: (i) node an in 2 months; (ii) node ad in 2 months; (iii) node dd in 2 months; (iv) node a in 1 month; (v) node d in 1 month; and (vi) today.)

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