Consider a two-period stock model over a period of 6 months, with interest rate 4%. The initial price of the stock is 4, while in each period the stock may either increase by a factor of 2 or decrease by a factor of 1/2. 21. (i) What are the risk neutral probabilities for this stock? Find the arbitrage free price of a call option on this stock with strike price 6. ili) A lookback call option with strike price K pays out nothing if the stock price never exceeded K over the lifetime of the option and pays out the difference between the maximum stock price and K if it did. Find the arbitrage free price of a lookback call option on this stock with strike price 6. 22. Repeat Question 21, but this time with three periods