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Mathematical Foundations of Regression Methods for the approximation of the Forward Initial Margin

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  • Lucia Cipolina Kun
  • Simone Caenazzo
  • Ksenia Ponomareva

Abstract

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.

Suggested Citation

  • Lucia Cipolina Kun & Simone Caenazzo & Ksenia Ponomareva, 2020. "Mathematical Foundations of Regression Methods for the approximation of the Forward Initial Margin," Papers 2002.04563, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2002.04563
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    References listed on IDEAS

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    1. Caspers, Peter & Giltinan, Paul & Lichters, Roland & Nowaczyk, Nikolai, 2017. "Forecasting initial margin requirements: A model evaluation," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 10(4), pages 365-394, October.
    2. Andrew Green & Chris Kenyon, 2014. "MVA: Initial Margin Valuation Adjustment by Replication and Regression," Papers 1405.0508, arXiv.org, revised Jan 2015.
    3. Anurag Sodhi, 2018. "American Put Option pricing using Least squares Monte Carlo method under Bakshi, Cao and Chen Model Framework (1997) and comparison to alternative regression techniques in Monte Carlo," Papers 1808.02791, arXiv.org.
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