Assume the Black-Scholes framework. You are given:

(i) The current dollar/euro exchange rate is 1.50$/€.

(ii) The volatility of the exchange rate is 20%.

(iii) The continuously compounded risk-free interest rate on dollars is 4%.

(iv) The continuously compounded risk-free interest rate on euros is 5%.

Consider a 6-month at-the-money dollar-denominated European put option on euros.

(a) Calculate the price of the put option.

(b) Determine whether the euro put above can be used to hedge against exchange rate risk faced by each of the following individuals living in the United States.

(1) Apple (Ambrose’s twin brother), a famous chef in Iowa City, regularly imports food raw materials from Europe, with the next order made in 6 months and settled in euros.

(2) Ambrosio (Ambrose’s another twin brother), fed up with his newly purchased iPhone XX, has decided to sell it to his aunt living in Europe for €500 in 6 months.

(c) The continuously compounded expected rate of appreciation of the dollar/euro exchange rate is 1.5%.

Calculate the true probability that the put option will be exercised.