You are interested in the computer company HAL computers. Its stock is currently priced at 9000 . The stock price is expected to either go up by \(25 \%\) or down by \(20 \%\) each six months. The annual risk free interest rate is \(20 \%\).

Your broker now calls you with an interesting offer.

You pay \(C_{0}\) now for the following opportunity: In month 6 you can choose whether or not to buy a call option on HAL computers with 6 months maturity (i.e. expiry is 12 months from now). This option has an exercise price of \(\$ 9000\), and costs \(\$ 1,500\). (You have an option on an option.)

1. If \(C_{0}\) is the fair price for this "compound option," find \(C_{0}\).

2. If you do not have any choice after 6 months, you have to buy the option, what is then the value of the contract?