Put Option

A put option is a financial contract that gives its holder the right, but not the obligation, to sell a set quantity of an underlying asset at a fixed price, called the strike price, on or before a specified expiry date. The buyer pays the seller, or writer, an upfront amount called the premium. If the asset's market price falls below the strike, the right to sell at the higher price becomes valuable; if it stays above, the buyer can let the option expire and loses only the premium.

Puts are one of the two basic types of options contract, the other being the call option, which gives the right to buy. They are traded on shares, stock indices, currencies, commodities and cryptocurrencies, both on regulated exchanges and over the counter, and they form part of the wider derivatives market. A shorter overview of the general idea is under option.

A put works much like insurance on something you own. Suppose you own a used car and pay a small fee for a promise that someone will buy it from you for a fixed amount any time in the next three months. If the car's value collapses, you use the promise and sell at the agreed price. If its value holds up, you never use the promise, and the fee is simply the cost of peace of mind.

The person who sold you that promise keeps the fee either way, but takes on the risk of having to buy your car for more than it is worth. That trade-off between a small certain cost and protection against a large loss is the heart of how puts are used.

At expiry, the value of a put to its holder is the amount by which the strike exceeds the market price, or zero if it does not:

The buyer's profit subtracts the premium paid:

• $K$ is the strike price.
• $S_T$ is the price of the underlying asset at expiry.
• $P$ is the premium paid for the option.

Suppose a trader buys a put on one share with a strike of 100 dollars for a premium of 5 dollars. If the share is at 80 dollars at expiry, the payoff is 100 − 80 = 20 dollars, and the profit is 20 − 5 = 15 dollars. If the share is at 110 dollars, the payoff is zero and the trader loses the 5-dollar premium. The break-even price is the strike minus the premium, 100 − 5 = 95 dollars. A put whose strike is above the current price is described as in the money.

A put's premium has two parts: intrinsic value, which is any amount by which it is already in the money, and time value, which reflects the chance that it will become more valuable before expiry. Prices rise with the strike price, with the time left to expiry and above all with expected volatility, since bigger swings make a large fall more likely. Higher interest rates tend to lower put prices slightly. The Black-Scholes model and its variants are the standard tools for calculating fair premiums, although traders often quote options by the volatility implied by their market price.

• Protection. An investor who holds shares or coins can buy puts to cap the loss from a fall, a form of hedging often called a protective put.
• Bearish bets. A trader expecting a decline can buy puts instead of short selling; the maximum loss is the premium, whereas a short position can lose without limit.
• Income. Sellers collect premiums in exchange for agreeing to buy the asset at the strike. Some investors sell puts on assets they would be happy to own at a lower price.
• Portfolio insurance. Funds buy puts on stock indices to limit losses during a bear market.

Bitcoin and ether options trade on specialist crypto derivatives exchanges and on regulated venues such as CME Group, and some decentralised platforms offer on-chain options through smart contracts. Crypto puts work the same way as equity puts but are usually far more expensive in premium terms because crypto prices swing more. The ratio of put to call trading volume is watched as one gauge of market sentiment, though it is a rough signal.

A put buyer's loss is limited to the premium, but premiums can expire worthless again and again, so repeated protection is costly. A put seller's potential loss is large: if the asset falls to zero, the seller must still buy at the strike. Exchanges therefore require sellers to post margin, and sharp falls can force sellers to add funds or close positions. Options also involve leverage, early-exercise rules that differ between American and European styles, and liquidity that can be thin away from popular strikes and dates. None of this is advice to trade.

• Options Industry Council