A put option's Value at expiry is the put's strike price less the underlying stock price. The Profit at expiry is its value, less the premium initially paid for the option.

Value = strike - stock price

Profit = (value at expiry - option cost) × (number of contracts × 100)
______ = ((strike - stock price) - option cost)
________ × (number of contracts × 100)

The Breakeven at expiry is the strike less the cost paid for the option, so will always be less than the underlying strike price when purchased.

Breakeven price = strike - option cost

To calculate profit prior to expiry is more in-depth.

The higher the chance the stock will close below the strike price, the higher the price of the option will be. Longer-dated expiries and puts with lower strike prices will almost always be worth more than nearer expiring options, or higher-striked puts.

Profit = ((strike price – stock price) - option cost + time value)
________ × (100 × number of contracts)

Our put calculator (above) will estimate the value of a long put at any stock price before or at expiry.

Related: What happens when options expire to ensure you capture the maximum profit

Profit increases linearly as the stock approaches $0, which is of course extremely rare, so while profit is capped, in practice there is no profit shelf as in other strategies such as spreads.

Given the relatively low price of purchasing an option compared to shorting a stock, long put strategies provide high return on risk. Loss is generally limited to the initial value of the option paid.

Put options gain value when the stock declines, whereas calls gain when the stock goes up*. Buying a put gives you the right to sell stock for a predetermined price, whereas buying a call gives you the right to buy the stock.

*Generalisation which holds unless there are sudden changes in market volatility.

This is because the contract is for the right to sell shares for an agreed price (the strike). The lower the stock price is compared to the agreed price, the more profitable it would be for you to exercise your option to sell at a price that is higher than the stock is worth.

No, you can buy put options without owning the shares of the underlying stock.

If you exercise the right to sell, then you will need to own stock, or your broker can buy stock at this point in time.

No, as the buyer of the contract you are entirely in control of whether or not to sell stock you may or may not have.

This is in contrast to a short call / naked call, where someone else has the right to buy stocks from you.