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A put option gives the holder the right but not the obligation to sell the underlying asset at the strike price. Therefore a put option is exercised when the price of the stock is below the strike price. The owner of a put option has a benefit when the price of the underlying falls as the holder is able to sell it at a higher price through option as compared to the market price. Premium has nothing to do in case of exercising the option. This is taken into account while calculating the net profit.
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