Problem 7 (Barrier options). (8 pts) Consider a two step binomial tree with the following parameters: S0=100,u=0.1,d=0.1 and R=0.03. Find the prices of a) (3 pts) A European knock-out call option with a strike price of 95 and a barrier of 90 . A knock-out option ceases to exist when the underlying asset price reaches a certain barrier. Therefore, if the stock price reaches 90 , the option no longer exists and the payoff is zero. b) (3 pts) A European knock-in call option with a strike price of 95 and a barrier of 90 . A knock-in option comes into existence only when the underlying asset price reaches a barrier. Therefore, if the stock price never reaches 90 , the option does not exist and the payoff is zero. c) (2 pts) Without using the binomial tree model, find the price of a European call option with a strike price 95 by your results in part (a) and (b)