Models

(h3) Linear
Most VAR models can easily handle linear instruments such as Equities and Forwards
Linear means that the change in the value of a position (in response to a change in the market price) is a constant proportion
A straight line relationship exists between movements in the price of the underlying instrument and the profit and loss.

(h3) Non Linear (convex)
VAR models that allow for a convexity adjustment can handle non linear instruments such as bonds.
For such instruments a curved (convex) line relationship exists between the price of the asset and the profit and loss

(h3) Non Linear
Variance-covariance is not suitable for options or embedded Options
Options respond differently to changes to the value of the underlying instrument depending on whether they "in-the-money", "at-the-money" or "out-of-the-money".
For options a kinked line represents the relationship between the underlying instrument and the profit and loss