Consider a non-dividend paying stock with S0 = 49, sigma = 0.20 per annum. The continuously compounded risk-free interest is r = 5% per annum. Consider a European call option with strike price K = 50, and maturity of 20 weeks (so that T = 0.3846 = 20/52).

a) Construct a two-step binomial tree of the stock price movement over the period of 20 weeks. Compute the appropriate parameters of the model, that is, u and d, and draw a binomial tree of the stock price movement.

b) Write down the equations that determine the replicating portfolio at both node u and d. Compute the deltaof the European call option at node u and d.

c) Compute the risk neutral probability at the initial node. Compute price of the European call option at the initial node.

d) Compute the price of a put option with the same strike price and maturity.