Consider a three-period (t=0,1,2) binomial structure for a stock, with initial stock price 0 = 100. Over each of the next two periods, the price is expected to go up by 10% or down by 10%. Each period is three months. The risk-free interest rate is 8% per annum, with discrete compounding. The stock pays no dividend. a) Taking the stock as underlying asset, what is the value of a 6-month at-the-money European call option? Use the risk neutral valuation approach. (4 points) b) Replicate the call option above at t=0, using the stock and the risk-free bond. (4 points) c) What is the value of a lookback option with the same terms? (hint: a lookback options exercise price is the lowest stock price on the path) (4 points)

4. (12 points) Consider a three-period (t=0,1,2) binomial structure for a stock, with initial stock price So 100. Over each of the next two periods, the price is expected to go up by 10% or down by 10%. Each period is three months. The risk-free interest rate is 8% per annum, with discrete compounding. The stock pays no dividend. a) Taking the stock as underlying asset, what is the value of a 6-month at-the-money European call option? Use the risk neutral valuation approach. (4 points) b) Replicate the call option above at t=0, using the stock and the risk-free bond. (4 points) c) What is the value of a lookback option with the same terms? (hint: a lookback option's exercise price is the lowest stock price on the path) (4 points)