HAL [6]

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 Co 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 Co is the fair price for this "compound option," find Co2. If you do not have any choice after 6 months, you have to buy the option, what is then the value of the contract?