A power call option pays off (max(ST-X, 0))2 at time T, where ST is the stock price at time T and X is the exercise price. A stock price is currently $54. It is known that at the end of one year it will be either $60 or $50. The risk-free rate of interest with continuous compounding is 6% per annum. Calculate the value of a one year power call option with an exercise price of $55.

a. What is the delta of the power call option? (sample answer: 1.55 or 0.55) b. What is the risk neutral probability of up movement? (sample answer: 55.50%) c. What is the value of the power option? (sample answer: $15.50)