Naming pattern: Measures with “Euler” behavior follow the name
pattern:Main Measure Name Euler.
Euler is one of the approaches implemented in the FRTB Accelerator to
decompose a non-linear measure down to additive components. For
instance, the Euler variation of the IMCC
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.