An one-year European call option has the strike price of $60. The underlying stock pays no dividend and currently sells for $70. One time step is six months long, and the stock price may move up or down by 10% in each step. The risk-free rate is 3% per annum.

(a) What is the risk-neutral probability of an increase in the stock price in each step? [5 points]

(b) What is the time-0 current price of the call? [6 points]

(c) Find the replicating portfolio that we construct in time 0 to generate the same value as the call six months later. [6 points]

(d) Suppose that risk-averse investors require the stock return to be 12% per annum. In the approach of Discounted Cash Flow, what is the discount rate for the call per annum? [7 points] (Hint: Use the replicating portfolio found in (c).)