Call Option

A call option is a contract that gives its buyer the right, but not the obligation, to buy an underlying asset at a fixed price, called the strike price, on or before a set expiry date. The buyer pays the seller, or writer, an upfront fee called the premium. If the asset's market price rises above the strike, the buyer can buy at the lower strike price and profit; if it does not, the buyer lets the option expire and loses only the premium. Calls are written on shares, indices, currencies, commodities, interest rates and, since the late 2010s, cryptocurrencies such as Bitcoin and ether.

A call is one of the two basic forms of options contract; the other is the put, which gives the right to sell. Options belong to the wider family of derivatives, whose value depends on another asset. Exchange-listed options in the United States are overseen by the Securities and Exchange Commission for securities options and by the Commodity Futures Trading Commission for options on futures and commodities.

Imagine putting down a small, non-refundable deposit to hold a house at today's price for three months. If house prices in the area jump, you can still buy at the agreed price, so your deposit was well spent. If prices fall, you walk away and lose only the deposit. A call option works the same way: the premium is the deposit, the agreed price is the strike, and the three months is the time until expiry.

The person who sells you the call is taking the other side of that bet. They keep the premium no matter what, but if the price shoots up they must hand over the asset at the agreed price, however high the market has gone. That is why the seller charges more for calls when markets are jumpy.

At expiry, a call is worth the amount by which the market price exceeds the strike, or nothing if the price is at or below the strike. The buyer's profit is that value minus the premium paid:

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

For example, a trader pays a premium of $4 for a call on a share with a strike of $100. If the share closes at $112 at expiry, the call is worth $12 and the profit is $12 − $4 = $8 per share. If the share closes at $98, the call expires worthless and the loss is the $4 premium. The break-even price is the strike plus the premium, here $104. A call whose strike is below the current price is "in the money"; one whose strike is above it is "out of the money". Options settled on exchanges usually cover a standard lot, such as 100 shares in the US equity market.

The premium has two parts. Intrinsic value is what the option would be worth if exercised immediately. Time value is the extra amount buyers pay for the chance that the price moves further in their favour before expiry. The main inputs are:

• Price and strike. The higher the underlying price relative to the strike, the more a call is worth.
• Time to expiry. Longer-dated calls cost more because there is more time for the price to rise.
• Volatility. Greater expected volatility raises the premium, since large upward moves become more likely while the buyer's loss stays capped.
• Interest rates and dividends. Higher rates slightly raise call values; expected dividends lower them.

The Black-Scholes model, published in 1973, was the first widely adopted formula for pricing European-style options, which can only be exercised at expiry. American-style options, which can be exercised at any time, are priced with variations such as binomial models.

Investors buy calls to gain upside exposure with a known maximum loss, using far less money than buying the asset outright. This built-in leverage magnifies percentage gains and losses. Sellers write calls to earn premium income; a "covered call" is written by someone who already owns the asset, which caps their upside in exchange for steady income, a form of selling volatility. Companies grant share options to staff, which are a form of call on the company's own stock. Calls are also combined with other options in spreads that limit both risk and reward, and are used for hedging short positions.

Crypto options trade on specialised derivatives exchanges and on regulated venues. The Chicago Mercantile Exchange lists options on its bitcoin and ether futures, and since 2024 US exchanges have listed options on spot bitcoin exchange-traded funds. On-chain options protocols in decentralized finance let users write and buy calls through smart contracts, though liquidity there is thinner. Because crypto prices are highly volatile, crypto call premiums tend to be much higher, as a share of the asset's price, than for most shares. The risks are also larger: writers of uncovered calls face theoretically unlimited losses, and offshore venues may not offer the investor protections of regulated markets.