1. a) After successfully completing your degree at ANU, you have decided not to follow Steves advice, and will start trading in options. Specifically, you want to start selling American futures options. The current spot price of copper is $7,500 per tonne, the futures price on copper is $8,300 per tonne and the risk-free rate of interest is 1.25% p.a. continuously compounded. The volatility of both the spot price and futures price on copper is 28% p.a. continuously compounded. Using the binomial option pricing model, if you sell an 18- month American call futures option on copper with a strike price of $7,200 per tonne what option premium would you receive. In providing your answer, you can assume there are two time steps of nine months each, and you must include a diagram of the binomial tree with all nodes clearly labelled. Assume there are no storage costs for copper. (8 marks)

2. b) You have been enjoying selling call futures options, and you now decide it is time to trade in more derivatives. Specifically, you have just sold 15-month European call options on 400 million USDs, with a strike price of 0.78 (1 USD equals 0.78 Australian dollars). The current exchange rate is 0.76 (1 USD equals 0.76 Australian dollars), the risk-free rate of interest in Australia is 1.25% p.a. continuously compounded and the risk-free rate of interest in the US is 0.25% p.a. continuously compounded. The volatility of the USD is 26% p.a. continuously compounded. You decide it would be good to implement a delta hedging strategy. How would you implement this delta hedging strategy? You can assume Australia is the home currency and the US is the foreign currency.