i) Using a four-step binomial tree calculate the price of a European nine month call option to buy 1 USD for 1 AUD (spend 10 minutes on this calculation). Prior to arriving at the lecture, using Bloomberg you identify the following information: 1 USD = 1.29 AUD, the volatility of the USD/AUD currency pair is 35% per annum, the US risk-free rate is 1.25% per annum with continuous compounding and the AUD risk-free rate is 1.50% per annum with continuous compounding. In addition, explain to students what happens when the number of steps in the binomial tree increases to a very large number.
ii) Using the same information as part i), estimate the price of an American nine month call option to buy 1 USD for 1 AUD.