Multi Step Binomial Tree: Consider again the at-the-money European call option with one year left to maturity written on a non-dividend paying stock. As in exercise 2, let todays stock price be 80 kr, the stock volatility be 30% and the risk free interest rate be 6%.

(a) Construct a one-year, five-step Binomial tree for the stock and calculate todays price of the European at-the-money call.

(c) The option can be replicated by a portfolio consisting of the stock and a risk-free asset. What is the replicating portfolio strategy of the call?

(d) Explain how the delta should change, as the stock price increase and check if this is indeed the case in your tree.