CallOption

CallOption is a financial derivative that gives the holder the right, but not the obligation, to buy a specified underlying asset at a predetermined price (the strike) within a set period. The underlying is typically shares, but may include indices, commodities, or other instruments. A call option is purchased by paying a premium to the seller, who has the obligation to deliver the asset if the option is exercised. American-style calls can be exercised at any time before expiration; European-style calls can be exercised only at expiration.

At expiration, the payoff to a long call is max(S-K, 0), where S is the market price of the underlying and K is the strike. The holder's profit equals max(S-K, 0) minus the premium paid. If the underlying price exceeds the strike, exercising is beneficial; otherwise the option expires worthless.

Pricing of call options uses models such as Black-Scholes or binomial trees. The theoretical value depends on current price, strike, time to expiration, volatility of the underlying, the risk-free rate, and expected dividends. Sensitivities are summarized by the Greeks, including delta, theta, gamma, vega, and rho.

Uses include speculation on rising prices, hedging against price declines, and income strategies such as covered calls. Common considerations include time decay, liquidity, and the risk of loss of the premium for buyers and potentially unlimited losses for sellers.

Example: stock trading at 110, strike 100, premium 5. If the stock ends at 120, the payoff is 20; profit is 20 minus 5 equals 15.