Consider a 4-period binomial model of option pricing. Let the current period be t = 0. Prices change at period t = 1, period t = 2 and period t = 3. Period t = 3 is the period in which the option expires. At t = 0, the price of the stock that the option is written on is $100. In each period the stock price may go up by 15 percent or down by 8 percent. Unless stated otherwise, the exercise price of the option is $105. The risk-free rate of borrowing and lending is 1 percent per period.

1. Draw a tree diagram that specifies all of the possible paths that the price of the underlying asset can take. At each node in the tree indicate what the price of the asset is.

2. Assume that the stock that the option is written on will not pay any dividends from t = 0 to t=3. Also assume that the option is a European call option.

2.a Draw a tree diagram and show at each node in the tree what portfolio of the stock and risk-free bonds will allow you to replicate the payoff on the option.

2.b On this tree diagram, identify the price for the option at each node.

3. Do the same thing that you did for question 2.b above for an American put option on a stock that pays no dividends. This time let the exercise price be $110.