A European put is available for purchase on the Stock Exchange. This put has strike price $20.50 and will mature in two time steps. The puts underlying asset is stock. The values of this stock are describe by Cox-Ross-Rubenstein notation with initial stock price S=$20.00, up factor u=1.15 and down factor d=0.90. The rate of return over each time step is a constant R=1.05.

(a) Plot the writer's payoff for the put at expiry against the stock price.

(b) Construct a two-step binomial pricing tree for the stock prices.

(c) Calculate the three possible maturity values of the put.

(d) Calculate the risk neutral probability for the two-step binomial model.

(e) Calculate all values of the European put in a two-step binomial model and construct the two-step binomial pricing tree for these put values.

(f) An American put has the same strike price, maturity time and underlying asset as the European put. Using a two-step binomial pricing model, calculate the premium of the American put. Assume that the stock pays no dividends during the next two time steps.