3. The current exchange rate between the Australian dollar and the Japanese Yen is AU$1 buys U94.35.

(a) Express this currency exchange in direct form.

(b) Using crr notation, the initial exchange rate X is your solution from part (a), the up factor is u = 1.06 and the down factor is d = 0.94. Construct a three-step binomial pricing tree for this exchange rate.

(c) Construct three-step binomial pricing trees for the following options, using the exchange rate in part (b) as the underlying asset. Take the domestic return over each time step to be Rd = 1.08 and the Japanese return over each time step to be Rf = 1.09.

i. A European call with strike rate k = 0.01080 (here, use face value F = U1).

ii. A European put with strike rate k = 0.01080 (here, use face value F = U1).

iii. Premiums of derivatives written on exchange rates are often expressed as a percentage per unit of the face value F. For both the call and the put, what are the premiums as a percentage per unit of the face value?

(d) An Australian company is expecting a payment of U50 million from a Japanese partner. The payment is expected in three time steps (at the same time the options described in part (c) will expire).

i. If the company does not buy a put or a call, then, in three time steps, what are the four possible amounts the Australian company could receive from its retail branch, in Australian dollars?

ii. To avoid potential losses, this Australian company buys a European put as described in part (c)c(ii) with face value F = U50 million. What is the premium of this put?

iii. Show that by buying the put, in three time steps this Australian company will receive at least F k = AU$540 000.

NB: Make sure that you clearly state which currency is being used for each of your answers to this question.