options

Options are financial derivatives that give the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price within a specified period. They are traded on stocks, indices, ETFs, commodities, and futures, and the buyer pays a premium for this right.

There are two main types: call options, which grant the right to buy the underlying asset at the strike price, and put options, which grant the right to sell at the strike price. American options can be exercised any time before or at expiration, while European options can be exercised only at expiration. Some options are settled in cash rather than through delivery of the underlying asset.

Key terms include the strike price, expiration date, and premium. An option’s value can be described as intrinsic value (the immediate exercise value) plus time value. A call option is in the money when the underlying price is above the strike; a put option is in the money when the underlying price is below the strike. Intrinsic value is max(0, S−K) for calls and max(0, K−S) for puts, where S is the underlying price and K is the strike price.

Pricing and risk are influenced by factors such as the underlying price, volatility, time to expiration, interest rates, and dividends. Traders refer to risk sensitivities known as the Greeks, including delta, gamma, theta, vega, and rho.

Options are used for hedging, income generation through writing options, or speculative bets on price movements and volatility. They carry risks, including the potential loss of the premium for buyers and potentially large obligations for sellers.