A derivative on a stock will expire exactly 6 months from now. The payoff of the derivative is given by:

Payoff= 120 120

=2 240 >120

where ST denotes the price of the stock on the expiry date.

The stock price today is 100.

On the expiry date, the stock price is expected to be either 150 or 80. The annual interest rate is 10% and compounded continuously. Using a two period model, find the price of the derivative.

Explain all your steps clearly.