I am given a question which I think is missing the necessary information to solve. The question is: Suppose a stock is valued at \$75 today. And the option will pay \$1 the first time the stock reaches \$100. Find the price of the option and the replicating portfolio.
First of all, only one state is given so you get infinite solutions for the possible numbers of stocks and bonds. Also, suppose we are replicating the option with stocks and bonds, the risk-free interest rate is not even given so how are we supposed to know the price of the bond at this future time. Is this question solvable with the information given?