Any trade that derives from an underlying asset, but does not involve the direct purchase or sale of that asset, is known as a derivative. Common classes of derivatives are forwards and futures, swaps and options. Derivatives are often divided into linear and nonlinear.

The simpler set of derivatives are linear products. This means that the payoff is related linearly to the spot price of the underlying asset. (We disregard unexpected or unknown extra payments, such as share dividends from this consideration.)

For example, suppose on 3 January 2009 you purchase a six-month forward silver contract at USD 17.05 per troy ounce. The profit or loss six months later is as shown:

Spot price on 3-Jul-09 | Profit per unit |
---|---|

15.05 | −2 |

16.05 | −1 |

17.05 | 0 |

18.05 | 1 etc. |

Clearly the profit is linearly related to spot price. The same is true for swaps.

When the payoff versus spot price is nonlinear for some or all spot prices then we say the trade is a nonlinear derivative. The most common nonlinear product is an option.

An option can be on any underlying financial or nonfinancial instrument. The option trade references the underlying instrument ...

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