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1. Numerical relationships.

Linear relationships are straight-line, or approximately straight-line.

Non-linear numerical relationships are all others.

Example - Shortcomings of climate change model include linear estimation
"A shortcoming of our model build so far is that some economic impacts are linearly estimated: non-linearities are not adequately captured.
... it’s not possible to estimate non-linear relationships between temperature increases and economic activity for most channels, especially for temperature increases that have not been observed yet.
We use multiplicative factors of 5 and 10 to simulate the increasing severity of outcomes from nonlinearities.
Importantly, the framework does not consider tipping points, events such as the partial disintegration of ice sheets, biosphere collapses or permafrost loss, that pose a threat of abrupt and irreversible climate change...
... other research suggests that if tipping points do happen, there could be an x8 increase in climate change associated economic damages."
Swiss Re Institute - The economics of climate change: no action not an option - April 2021

2. Interest rate derivatives.

Describing interest rate derivatives that are not linear.

Linear interest rate derivatives are ones whose values are determined primarily by the reference interest rate, in an approximately proportional relationship.

Non-linear interest rate derivatives are all other interest rate derivatives.

Examples of non-linear interest rate derivatives include interest rate options, and swaptions.

See also