A closed form model-free approximation for the Initial Margin of option portfolios

TL;DR

This paper introduces a novel, model-free approximation formula for initial margin calculation of option portfolios, improving accuracy over traditional methods and leveraging neural-SDE models for explicit VaR formulas.

Contribution

It derives a new short-horizon VaR approximation formula that is model-free and compares favorably to existing industry methods, also providing explicit formulas within a neural-SDE framework.

Findings

The new approximation outperforms classical Filtered Historical Simulation VaR in experiments.

A quasi-explicit VaR formula is obtained for neural-SDE models.

The approach simplifies initial margin computation with promising accuracy.

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.