Definition
A put option gives its buyer the right, but not the obligation, to sell a set quantity of the underlying asset at the strike price on or before expiration, in return for a premium.
How it works
At expiry a put has value only if the underlying price is below the strike, and its payoff per unit is the gap between the strike and that price. The buyer's break-even is the strike minus the premium. Because a price cannot fall below zero, a put's maximum payoff per unit is the strike.
Buyers use puts to hedge a holding, like insurance with a premium cost, or to take a falling-price view with a defined maximum loss. A put seller collects the premium but may have to buy the underlying at the strike, so a sharp fall can cause losses far larger than the premium.
Formula / convention
Payoff per unit at expiry = max(K − S, 0); Profit per unit = Payoff − Premium; Break-even price = K − Premium (S = underlying price at expiry, K = strike); multiply per-unit amounts by the contract multiplier and number of contracts
Illustrative example
A fictional put on Sample Co has a HK$40 strike and a HK$1.50 premium per share and covers 2,000 shares, so the buyer pays HK$3,000. If the share closes at HK$34 at expiry, the payoff is (40 − 34) × 2,000 = HK$12,000 and the profit after premium is HK$9,000. The break-even price is 40 − 1.50 = HK$38.50, and if the share closes at HK$40 or above the loss is the HK$3,000 premium.
What to watch for
A put loses value as time passes if the underlying stays above the strike, and the entire premium can be lost; selling puts can lead to very large losses if the underlying collapses.