The time value of the option is greatest when the stock prices near the exercise price because it will make the intrinsic value of the share lowest and intrinsic value of the share is is the value of difference between the strike price and the current market price, so, the nearest the the strike price is to the the current market price, the lowest will be the intrinsic value and the highest will be the time value of the option.
When the option will be deep out of the money or deep in the money then the time value of money would be lowest, because the difference between strike price and the current market price should be highest and the intrinsic value will also be highest, so the time value of option will be lowest
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