The stock price is currently at $50 per share. In one month it is expected to either go up to $62.5 or down to $40. An at-the-money European call option with 2 monthsto maturity is trading on this stock. Risk-free asset pays 0.5% interest rate per month.

a) Find u, d, and R to plug into the binomial tree formula.

b) Based on u, d, and R build the binomial tree for the stock.

c) Find the terminal option prices c_uu, c_ud, and c_dd.

d) Using the binomial formula, find c_u, c_d, and c.

e) Find the option delta at every node of the tree (except the terminal nodes).

f) If you have written 100 call option contracts, how many shares to you need today to hedge the delta risk?

g) In the up state one year from now, how should you adjust your hedge? What about the down state one year from now?