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Mathematical Foundations of Regression Methods for Approximating the Forward Initial Margin

Lucia Cipolina-Kun, Simone Caenazzo and Ksenia Ponomareva
The Journal of Derivatives Winter 2022, 30 (2) 127-140; DOI: https://doi.org/10.3905/jod.2022.30.2.127
Lucia Cipolina-Kun
is a PhD Candidate in the Department of Electrical and Electronic Engineering at the University of Bristol in Bristol, UK
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Simone Caenazzo
is a senior quant at Riskcare Ltd., Quantitative Analytics Team in London UK
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Ksenia Ponomareva
is a partner at Riskcare Ltd., Quantitative Analytics Team in London UK
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Abstract

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.

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The Journal of Derivatives: 30 (2)
The Journal of Derivatives
Vol. 30, Issue 2
Winter 2022
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Mathematical Foundations of Regression Methods for Approximating the Forward Initial Margin
Lucia Cipolina-Kun, Simone Caenazzo, Ksenia Ponomareva
The Journal of Derivatives Nov 2022, 30 (2) 127-140; DOI: 10.3905/jod.2022.30.2.127

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Mathematical Foundations of Regression Methods for Approximating the Forward Initial Margin
Lucia Cipolina-Kun, Simone Caenazzo, Ksenia Ponomareva
The Journal of Derivatives Nov 2022, 30 (2) 127-140; DOI: 10.3905/jod.2022.30.2.127
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  • Article
    • Abstract
    • DESCRIPTION OF THE FORWARD INITIAL MARGIN PROBLEM
    • REGRESSION METHODS FOR THE APPROXIMATION OF THE FORWARD INITIAL MARGIN
    • CONDITIONAL EXPECTATIONS AS ORTHOGONAL PROJECTIONS ON HILBERT SPACES
    • ENDNOTES
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