Standard formula does not explicitly allow for non-linearity. Standard formula allows for non-separability to a degree when aggregating risks using correlation matrices.
Internal model firms will have flexibility in how they address non-linearity and non-separability, and approaches will vary between firms. I suspect [but cannot say for certain] that details of how its done is outside scope of core reading/exam. If you are interested in learning more, try searching for and reading up on the "Equivalent Scenario" or on "Copulas".
Last edited: Sep 28, 2017