A Closed Form Model-Free Approximation for the Initial Margin of Option Portfolios

35 Pages Posted: 26 Jun 2023

See all articles by Arianna Mingone

Arianna Mingone

Ecole Polytechnique de Paris (CMAP); Zeliade Systems

Claude Martini

Zeliade Systems

Date Written: June 22, 2023

Abstract

Central clearing counterparty houses (CCPs) play a fundamental role in mitigating the counterparty risk for exchange traded options. CCPs cover for possible losses during the liquidation of a defaulting member's portfolio by collecting initial margins from their members. In this article we analyze the current state of the art in the industry for computing initial margins for options, whose core component is generally based on a VaR or Expected Shortfall risk measure. We derive an approximation formula for the VaR at short horizons in a model-free setting. This innovating formula has promising features and behaves in a much more satisfactory way than the classical Filtered Historical Simulation-based VaR in our numerical experiments. In addition, we consider the neural-SDE model for normalized call prices proposed by [Cohen et al., arXiv:2202.07148, 2022] and obtain a quasi-explicit formula for the VaR and a closed formula for the short term VaR in this model, due to its conditional affine structure.

Keywords: Initial Margin, Options, CCPs, FHS, VaR, Market risk

JEL Classification: C14, C18, G10, G23

Suggested Citation

Mingone, Arianna and Martini, Claude, A Closed Form Model-Free Approximation for the Initial Margin of Option Portfolios (June 22, 2023). Available at SSRN: https://ssrn.com/abstract=4488025 or http://dx.doi.org/10.2139/ssrn.4488025

Arianna Mingone (Contact Author)

Ecole Polytechnique de Paris (CMAP) ( email )

Paris
France

Zeliade Systems ( email )

Paris
France

Claude Martini

Zeliade Systems ( email )

Paris
France

HOME PAGE: http://www.zeliade.com

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