As a financial analyst at Citibank Derivative Trading desk, you have collected data for a power option. A power call option pays off (max(S_T-X, 0))² at time T, where S_T is the stock price at time T and X is the exercise price. A stock price is currently $60. It is known that at the end of one year it will be either $66 or $54. The risk-free rate of interest with continuous compounding is 5% per annum. Calculate the value of a one year power call option with an exercise price of $60.

What is the delta of the option ? What is the risk neutral probability of up move ? What is the value of the option ?