When are puts (long or short) considered in-the-money?

Puts are considered in-the-money when the market price of the underlying asset is below the strike price. This is because a put option gives the holder the right to sell the underlying asset at the strike price. If the market price is lower than the strike price, the holder can sell the asset for more than its market value, thereby making a profit if they exercise the option. This situation reflects the intrinsic value of the put option, indicating that it has real value in the current market conditions.

When evaluating other choices, the situation where the market price equals the strike price does not provide any advantage to the put holder, as there would be no profit in exercising the option. If the market price is above the strike price, the put option would be out-of-the-money, as it would not be beneficial to sell the asset at the higher strike price compared to the market price. Lastly, the reference to the strike price being less than the premium does not determine whether the put is in-the-money; this relates to the profitability of the option rather than its intrinsic value.