You sell a European option with maturity 1 month, strike 30, and with an underlying assent of current value 60. The risk-free interest rate is 5%. In 1 month, the value of the underlying asset can either 72 with probability 60% or 56 with probability 40%.

a) Compute the risk-neutral probabilities

b) Compute the price of the option

c) Find the replicating strategy

d) Compute the price of the option if the real probabilities are 80% to go up and 20% to go down.