Suppose that we are in a two-period world (t = 0, 1, 2). The current (t = 0) price of a stock

is $100. Each period, its value can either increase by 10% or decrease by 5%. The risk-free

rate is 2% per period.

11. Draw a tree of the possible future stock prices.

2. What is the value of a European call option on the stock with strike price of $110 and

a maturity of t = 2?

3. What is the value of a derivative security which pays the maximum stock price achieved

by the stock over t = 0, 1, 2? (i.e., If the stock price path is $100, $110, $104.50, then

the payoffff to this security is $110. If the stock price path is $100, $95, $104.50, then

the payoffff is $104.50.) The payment occurs at t = 2.

Hint: Start by drawing the tree with possible payoffffs at t = 2. Then, you can use the

replication method from class.