# Non-linear

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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.