A stock sells at $50. The price will be either $57.5 or $47.5 three months from now. Assume the risk-free rate is 12% per annum with continuous compounding. Consider a call option on the stock that has a strike price of $52.5 and a maturity of 3 months.

a) Find a portfolio of the stock and bonds such that buying the call is equivalent to holding the portfolio. What is the cost of the portfolio? And what is the call price?

b) What position in the stock is necessary to hedge a long position in one call option?

c) What is the risk-neutral probability of the stock rising to $57.5?