- published: 29 Apr 2016
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A derivative instrument is a contract between two parties that specifies conditions (especially the dates, resulting values of the underlying variables, and notional amounts) under which payments are to be made between the parties.
Under US law and the laws of most other developed countries, derivatives have special legal exemptions that make them a particularly attractive legal form through which to extend credit. However, the strong creditor protections afforded to derivatives counterparties, in combination with their complexity and lack of transparency, can cause capital markets to underprice credit risk. This can contribute to credit booms, and increase systemic risks. Indeed, the use of derivatives to mask credit risk from third parties while protecting derivative counterparties contributed to the financial crisis of 2008 in the United States.
Financial reforms within the US since the financial crisis have served only to reinforce special protections for derivatives, including greater access to government guarantees, while minimizing disclosure to broader financial markets.
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function.
The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.