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

Paper: arXiv 2306.16346

Authors: Claude Martini, Arianna Mingone

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative closed-form, model-free approximation for short-horizon VaR tailored for Initial Margin calculations, supplemented by a neural-SDE formulation. It strikes a strong balance between advanced mathematical derivation and practical quantitative finance application, though empirical validation is focused primarily on controlled numerical experiments.

Research Flowchart

  flowchart TD
    A[Research Goal: Model-free Initial Margin / VaR approximation for option portfolios] --> B[Inputs: Option Portfolio Data & Risk Measures VaR / Expected Shortfall]
    B --> C[Method 1: Derive short-horizon VaR approximation formula in a model-free setting]
    B --> D[Method 2: Apply Neural-SDE model for normalized call prices]
    C --> E[Numerical Experiments & FHS-VaR Benchmark Comparison]
    D --> E
    E --> F[Outcomes: Closed-form short-term VaR & quasi-explicit VaR outperforming classical FHS]