Currently, US $1 buys AU $1.25. In one month US $1 will buy either AU $1.30 or AU $1.15. The return in Australia over one month is currently R_d = 1.05 and the return in the USA over one month is currently R_f = 1.055.

(a) What is the risk neutral probability over one month?

(b) A European call is available with maturity in one month, strike rate k = 1.20, and $US as the underlying asset. Use the one-step binomial pricing formula to calculate the premium of this call as a percentage of the face value.

(c) In one month an Australian company needs to pay its US supplier US $500,000. The Australian company also buys the call described in (b) with face value US $500,000.

(i) In one month, how much will US $500,000 be worth in Australian dollars?

(ii) In Australian dollars, what premium does the Australian company pay for the call?

(iii) In one month, what are the company's two possible payoffs in Australian dollars?