1. Alumina Limited (AWC), is an Australian company that (partially) owns a number of mining and smelting operations globally; in Australia, this includes a number of Bauxite mines, and refineries that produce alumina and aluminium. At the time of writing, the share price for AWC is $1.56. Consider this to be time zero. You wish to write a European put on AWC shares, with strike price $1.50, that expires in 4 (monthly) time steps. Assume that the return rate on a bank investment over each time step is R=1.01. (a) Use CRR notation to construct a four-step binomial pricing tree for an AWC share, with u = 1.25 and d=1/u. (b) Find the premium of the put by calculating the risk neutral probabilities and then constructing a four-step binomial pricing tree. (c) Use put-call parity to find the premium of a European call with the same under- lying asset, strike price and expiry as the European put. Use PVo(K) = K/R. (d) Calculate all state prices at the put's expiry. That is, calculate all \(4, j) for j = 0,1,...,4. (e) Use the state prices 1(4, j) to calculate the premium of the European put. Com- pare this premium to the premium calculated in part (b)