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

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  • 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.

Suggested Citation

  • Claude Martini & Arianna Mingone, 2023. "A closed form model-free approximation for the Initial Margin of option portfolios," Papers 2306.16346, arXiv.org.
    • Handle: RePEc:arx:papers:2306.16346
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    References listed on IDEAS

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    1. Pedro Gurrola-Perez & David Murphy, 2015. "Filtered historical simulation Value-at-Risk models and their competitors," Bank of England Staff Working Paper series 525, Bank of England.
    2. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2020. "Detecting and repairing arbitrage in traded option prices," Papers 2008.09454, arXiv.org.
    3. Berg, C. & Vignat, C., 2010. "On the density of the sum of two independent Student t-random vectors," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1043-1055, July.
    4. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2020. "Detecting and Repairing Arbitrage in Traded Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(5), pages 345-373, September.
    5. Giovanni Barone-Adesi & Kostas Giannopoulos, 2001. "Non parametric VaR Techniques. Myths and Realities," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(2), pages 167-181, July.
    6. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
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