This given statement is not true because every American option is not deep in the money and they are not exercised every time because there are many times when the strike price of the call option is not crossed by the market price of the share, and in those cases even American options are lapsed onto the maturity
These options are even not exercisable and they can easily come out of the money option if the share price is moving in adverse direction, which is following according to the call holder, and it will be leading to lapse of these call option because they cannot be exercised due to strike price not getting triggered by current market price.
So I do not agree with this statement of the American call option investor.
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