In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements:

A derivative's value depends on the performance of the underlier, which can be a commodity (for example, corn or oil), a financial instrument (e.g. a stock or a bond), a price index, a currency, or an interest rate.

Derivatives can be used to insure against price movements (hedging), increase exposure to price movements for speculation, or get access to otherwise hard-to-trade assets or markets. Most derivatives are price guarantees. But some are based on an event or performance of an act rather than a price. Agriculture, natural gas, electricity and oil businesses use derivatives to mitigate risk from adverse weather. Derivatives can be used to protect lenders against the risk of borrowers defaulting on an obligation.

Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the 2008 financial crisis, there has been increased pressure to move derivatives to trade on exchanges.

Derivatives are one of the three main categories of financial instruments, the other two being equity (i.e., stocks or shares) and debt (i.e., bonds and mortgages). The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. However, Aristotle did not define this arrangement as a derivative but as a monopoly (Aristotle's Politics, Book I, Chapter XI). Bucket shops, outlawed in 1936 in the US, are a more recent historical example.

Derivatives are contracts between two parties that specify conditions (especially the dates, resulting values and definitions of the underlying variables, the parties' contractual obligations, and the notional amount) under which payments are to be made between the parties. The assets include commodities, stocks, bonds, interest rates and currencies, but they can also be other derivatives, which adds another layer of complexity to proper valuation. The components of a firm's capital structure, e.g., bonds and stock, can also be considered derivatives, more precisely options, with the underlying being the firm's assets, but this is unusual outside of technical contexts.

From the economic point of view, financial derivatives are cash flows that are conditioned stochastically and discounted to present value. The market risk inherent in the underlying asset is attached to the financial derivative through contractual agreements and hence can be traded separately. The underlying asset does not have to be acquired. Derivatives therefore allow the breakup of ownership and participation in the market value of an asset. This also provides a considerable amount of freedom regarding the contract design. That contractual freedom allows derivative designers to modify the participation in the performance of the underlying asset almost arbitrarily. Thus, the participation in the market value of the underlying can be effectively weaker, stronger (leverage effect), or implemented as inverse. Hence, specifically the market price risk of the underlying asset can be controlled in almost every situation.

There are two groups of derivative contracts: the privately traded over-the-counter (OTC) derivatives such as swaps that do not go through an exchange or other intermediary, and exchange-traded derivatives (ETD) that are traded through specialized derivatives exchanges or other exchanges.