PT  - JOURNAL ARTICLE
AU  - Lucia Cipolina-Kun
AU  - Simone Caenazzo
AU  - Ksenia Ponomareva
TI  - Mathematical Foundations of Regression Methods for Approximating the Forward Initial Margin
AID  - 10.3905/jod.2022.30.2.127
DP  - 2022 Nov 30
TA  - The Journal of Derivatives
PG  - 127--140
VI  - 30
IP  - 2
4099  - https://pm-research.com/content/30/2/127.short
4100  - https://pm-research.com/content/30/2/127.full
AB  - The modelling of forward initial margin poses a challenging problem, as it requires the implementation of a nested Monte Carlo simulation, which is computationally intractable. Abundant literature has been published on approximation methods aiming to reduce the dimensionality of the problem, the most popular ones being the family of regression methods. This article describes the mathematical foundations on which these regression approximation methods lie. Mathematical rigor is introduced to show that, in essence, all methods are performing orthogonal projections on Hilbert spaces, while simply choosing a different functional form to numerically estimate the conditional expectation. The most popular methods in the literature so far are covered here. These are polynomial approximations, kernel regressions, and neural networks.