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A derivative is a financial instrument with a value that depends on (or derives from, hence the name) the value of another asset, known as the underlying.
These underlyings may be of a wide range of types: interest rates, stocks, currencies, financial indexes, commodity prices, etc. Derivatives can be used to hedge the price risk of the underlying assets, or they may be traded in an effort to profit from changes in their value.
Derivatives may be traded on organized financial markets (these are known as quoted derivatives) or outside of them (known as over-the-counter or OTC derivatives).