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 $25. It is known that at the end of one year it will be either $30 or $20. The risk-free rate of interest with continuous compounding is 7.5% per annum. Calculate the value of a one year power call option with an exercise price of $25.

a. What is the delta of the power call option?(sample answer: 0.75)

b. What is the risk neutral probability of up movement?(sample answer: 0.75)

c. What is the value of the power option?(sample answer: $15.75)