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Detecting and Repairing Arbitrage in Traded Option Prices

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  • Samuel N. Cohen
  • Christoph Reisinger
  • Sheng Wang

Abstract

Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e., removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimize prices’ changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real-world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:27:y:2020:i:5:p:345-373
    DOI: 10.1080/1350486X.2020.1846573
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    Citations

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    Cited by:

    1. Ariel Neufeld & Julian Sester, 2023. "Neural networks can detect model-free static arbitrage strategies," Papers 2306.16422, arXiv.org, revised Aug 2024.
    2. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    3. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Hedging option books using neural-SDE market models," Papers 2205.15991, arXiv.org.
    4. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.
    5. Claude Martini & Arianna Mingone, 2023. "A closed form model-free approximation for the Initial Margin of option portfolios," Papers 2306.16346, arXiv.org.
    6. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    7. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    8. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2021. "Arbitrage-free neural-SDE market models," Papers 2105.11053, arXiv.org, revised Aug 2021.
    9. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
    10. Samuel N. Cohen & Derek Snow & Lukasz Szpruch, 2021. "Black-box model risk in finance," Papers 2102.04757, arXiv.org.
    11. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    12. Yannick Limmer & Blanka Horvath, 2023. "Robust Hedging GANs," Papers 2307.02310, arXiv.org.

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