2. Suppose you are given the following data. The risk-free interest rate is 4%. The stock price follows: dSt = μSt + σStdWt (124) The percentage annual volatility is 18% a year. The stock pays no dividends and the current stock price is 100. Using these data, you are asked to calculate the current value of a European call option on the stock. The option has a strike price of 100 and a maturity of 200 days.

(a) Determine an appropriate time interval Δ, such that the binomial tree has five steps.

(b) What would be the implied u and d?

(c) What is the implied “up” probability?

(d) Determine the binomial tree for the stock price St.

(e) Determine the tree for the call premium Ct.