Two Step Binomial Tree: Consider again the at-the-money European call option with six months left to maturity written on a non-dividend paying stock. Let today's stock price be 80 kr and the stock volatility be 35%. Furthermore let the risk free interest rate be 8%.

(a) Construct a two-step Binomial tree for the stock.

(b) Use your stock tree in exercise (a) to calculate today's price of the European call.

(c) Consider a European at-the-money put option with six months left to maturity written on the stock depicted in exercise (a). Calculate today's price of this option.

(d) Explain how the at-the-money European call and the European put can be combined to a straddle. Calculate the cost of entering into the straddle, and draw both the payoff and the profit diagram.

(e) Consider an American at-the-money put option with six months left to maturity written on the stock depicted in exercise (a). Calculate today's price of this option.

(f) Consider a European derivative written on the stock depicted in exercise (a). This derivative will pay out an amount equal to the stock price in six months, if the stock price in six months is above 82 kr and zero otherwise. Calculate today's price of the derivative.