The domestic risk-free rate is 3% per annum, the foreign risk-free rate is 5% per annum, the exchange rate volatility is 12% and the time to maturity is 15 months. Interest rates are continuously compounded.

(i) Use a three-time-step tree to value an at-the-money American put option on a currency when the initial exchange rate is 1.2. [10%]

(ii) Calculate the option at t = 0 and after the first 5 months. [10%]

(iii) Suppose the exchange rate increases after 5 months. Explain how a financial institution would hedge a short position in the option in the first 5 months. How would you answer change if the exchange rate decreases after 5 months?