Consider a Binomial model in which the stock price can either go up by a factor u or down by a factor d and the risk free interest rate is r.

(a) Show that the risk neutral probability of an up movement is q = ert d ud

(b) Consider a two step Binomial model in which each time step is 4months, r = 0.05, u = 1.105, d = 0.905 and initial stock price S0 = 30. Find the value of a European call and put option with 1 strike price P30 maturing in 8months. Show that the put-call-parity is satised.