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 months to 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 cuu, cud, and cdd.
d. Using the binomial formula, find cu, cd, 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?
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