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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

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 $45. It is known that at the end of one year it will be either $54 or $36. 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 $50. What is the delta of the option ? What is the risk neutral probability of up move ? What is the value of the option ?

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