2. (13 pts) You can do part (b) of this problem in Excel a) Write the payoff functions for the European and American up-and-in barrier put option with barrier Draw a hypothetical graph representing a stock price evolution such that the option never becomes active. Clearly mark the axes and all important points b) Use the step binomial tree to price the up-and-in barrier put options (European style and American style, separately). Assume that the spot price is $105. The strike is $101. The barrier is $106. The time to maturity is 1 year. Risk-free rate is 5% with the annual compounding, the stock price goes up or down by 20 c) Is the European up-and-in barrier put option priced higher or lower than the same option whout barrier? 2. (13 pts) You can do part (b) of this problem in Excel a) Write the payoff functions for the European and American up-and-in barrier put option with barrier Draw a hypothetical graph representing a stock price evolution such that the option never becomes active. Clearly mark the axes and all important points b) Use the step binomial tree to price the up-and-in barrier put options (European style and American style, separately). Assume that the spot price is $105. The strike is $101. The barrier is $106. The time to maturity is 1 year. Risk-free rate is 5% with the annual compounding, the stock price goes up or down by 20 c) Is the European up-and-in barrier put option priced higher or lower than the same option whout barrier