> ## Documentation Index
> Fetch the complete documentation index at: https://docs.activeviam.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Euler

export const productName = "Atoti FRTB";

## Euler capital allocation

Naming pattern: Measures with "Euler” behavior follow the name
pattern:*Main Measure Name* Euler.

Euler is one of the approaches implemented in {productName} to
decompose a non-linear measure down to additive components. For
instance, the Euler *variation* of the [IMCC](./imcc-ima)
measure is called IMCC (Euler): the latter enables you to allocate a
result (for instance, at firm level) down to individual components
(typically, desks).

## Overview of Euler Calculations

The theory behind Euler Calculations is based on these facts:

* Use of Euler’s theorem of homogeneous functions

* Capital Charges are homogeneous functions of degree 1

* Euler Capital Allocation is the evaluation of the derivative on a
  sub-portfolio

## Analytical vs Numerical Euler

The difference between Analytical and Numerical Euler is in how the
calculations are performed:

* For Analytical Euler, we differentiate the functions and evaluate
  the derivative (this gives the exact value).

* For Numerical Euler, we use the Existing Capital Charge calculations
  to numerically approximate the derivative.

Follow this link to see the measures with the described behavior: [Euler Measures](./euler).

In both methods the charge computed at [ReferenceLevel](./referencelevel) is decomposed into additive components.
Additionally, the impact of query filters on the results can be controlled using [ReferenceLevelVisualTotalsMode](./referencelevelvisualtotalsmode).