q-fin updates on arXiv.org
Wed, 12 Feb 2020 06:01:22 GMT language
Abundant literature has been published on approximation methods for the
forward initial margin. The most popular ones being the family of regression
methods. This paper describes the mathematical foundations on which these
regression approximation methods lie. We introduce mathematical rigor to show
that in essence, all the methods propose variations of approximations for the
conditional expectation function, which is interpreted as an orthogonal
projection on Hilbert spaces. We show that each method is simply choosing a
different functional form to numerically estimate the conditional expectation.
We cover in particular the most popular methods in the literature so far,
Polynomial approximation, Kernel regressions and Neural Networks.