American Call Vs European Call

thunderbird

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Why is the value of the American call same as the value of the European Call on a non-dividend paying sock?
 
Ill try if a stock is going to pay a dividend you would want to hold shares in order to recieve the dividend therefore you would like to exercise your call option early and convert into shares(hold shares).because of this option price of american may increase as compared to european.if a stock does not pay dividend no point exercising early therefore value is same.
 
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