A European put written on shares has strike price $26 and expires in four time steps. Using crr notation, the underlying share prices are calculated using S = $25, u = 1.2 and d = 1/u . The return on a bank investment over each time step is R = 1.05 .

(a) Construct a four-step binomial pricing tree for the underlying asset.

(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 underlying asset, strike price and expiry as the European put. Use pv0(K) = K/R4 .

(d) Calculate all state prices at the puts expiry. That is, calculate all (4, j) for j = 0, 1, . . . , 4 .

(e) Use the state prices (4, j) to calculate the premium of the European put. Compare this premium to the premium calculated in part (b).