RT Journal Article
SR Electronic
T1 Mathematical Foundations of Regression Methods for Approximating the Forward Initial Margin
JF The Journal of Derivatives
FD Institutional Investor Journals
SP 127
OP 140
DO 10.3905/jod.2022.30.2.127
VO 30
IS 2
A1 Lucia Cipolina-Kun
A1 Simone Caenazzo
A1 Ksenia Ponomareva
YR 2022
UL https://pm-research.com/content/30/2/127.abstract
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.