1. Suppose the current price of a stock is $100 and every 6 months it may increase by 30% with a probability of 60% or decrease by 20% with a probability of 40%. The stock does not pay dividends over the next year. The risk free interest rate is constant and 5% (c.c.). (a) Use a binomial tree to determine the price of a floating strike Asian call option with 1-year maturity. The floating strike Asian call pays upon exercise ST - Saverage, where ST is the stock price at maturity T = and the strike price Saverage is an arithmetic average of the stock price over the lifetime of the option. (b) Use a binomial tree to determine the price of an at-the-money fixed strike Asian call option with 1-year maturity. The fixed strike Asian call pays upon exercise Saverage K, where K is the strike price and Saverage is an arithmetic average of the stock price over the lifetime of the option. (c) Use a binomial tree to determine the price of a lookback (or no-regret) call option with 1-year maturity. The lookback call pays upon exercise ST-min {S, : 7 [t,T]}, where min {S+ : T = [t, T]} is the smallest value the stock price takes over the life- time of the option. (d) Use a binomial tree to determine the price of an at-the-money knock-out barrier call option with 1-year maturity and a barrier at $90. A knock-out Barrier call option pays upon exercise the difference between the stock price at maturity and the strike, unless the stock price crosses the barrier price at any time during the life of the option, in which case the option expires worthless. (e) Use a binomial tree to determine the price of an at-the-money knock-in barrier call option with 1-year maturity and a barrier at $90. A knock-in barrier call option pays upon exercise the difference between the stock price at maturity and the strike, if and only if the stock price crosses the barrier price at any time during the life of the option.