Suppose the current exchange rate for USD/AUD is 0.73508. There is a European call option for buying AUD at price 0.75000, with 3 months until maturity. The interest rate for the underlying currency, AUD, is 2.25% p.a. and for the counter currency, USD, is 0.25% p.a. It is estimated that the volatility of the exchange rate is 20% over this period. For the purposes of this question, please use 360 days as one year.
(a) Please find the value of this call option, showing all steps.
(b) If you see that such an option is on sale in the market at USD1.80 cents, will it represent a buying opportunity?
(c) Suppose everything is the same as in Part (a), except that the exchange rate is 0.75, so that the option is at-the-money. What will be the price of this call? Show all your steps.
(d) Suppose everything is the same as in Part (a), find the value of this option if the time to expiry is 6 months instead. Show all your steps.
(e) Suppose everything is the same as in Part (a), find the value of the option if the volatility is 30% instead of 20%. Show all your steps.
(f) Suppose everything is the same as in Part (a), find the value of this option if the US interest rate rises to 0.5%. Does the option price rise or fall? Show all your steps.
(g) Suppose everything is the same as in Part (a), what will the option premium be if the strike price is 0.72 instead? Show all your steps.