(A) A stock price is currently AUD 50 and it is known that at the end of three months it will be either AUD 54 or AUD 46. We are interested in valuing a European call option.

(i) When the risk-free rate is 12% per annum; Apply stock-option replicating portfolio strategy to value this European call option when the strike is AUD 52.

(ii) If the delta of the above European call is 0.02, what is the delta of the European put for the same strike and maturity?

(B) A stock price is currently AUD 70; the risk-free rate is 5% and the volatility is 30%. What is the value of a two-year American put option with a strike price of AUD 72? (Hint: Assume there are two-time steps)