IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.14980.html

Selective Forgetting in Option Calibration: An Operator-Theoretic Gauss-Newton Framework

Author

Listed:
  • Ahmet Umur Ozsoy

Abstract

Calibration of option pricing models is routinely repeated as markets evolve, yet modern systems lack an operator for removing data from a calibrated model without full retraining. When quotes become stale, corrupted, or subject to deletion requirements, existing calibration pipelines must rebuild the entire nonlinear least-squares problem, even if only a small subset of data must be excluded. In this work, we introduce a principled framework for selective forgetting (machine unlearning) in parametric option calibration. We provide stability guarantees, perturbation bounds, and show that the proposed operators satisfy local exactness under standard regularity assumptions.

Suggested Citation

  • Ahmet Umur Ozsoy, 2025. "Selective Forgetting in Option Calibration: An Operator-Theoretic Gauss-Newton Framework," Papers 2511.14980, arXiv.org.
    • Handle: RePEc:arx:papers:2511.14980
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.14980
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    2. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    3. Maxim Ulrich & Lukas Zimmer & Constantin Merbecks, 2023. "Implied volatility surfaces: a comprehensive analysis using half a billion option prices," Review of Derivatives Research, Springer, vol. 26(2), pages 135-169, October.
    4. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    5. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ruan, Xinfeng & Zhang, Jin E., 2021. "The economics of the financial market for volatility trading," Journal of Financial Markets, Elsevier, vol. 52(C).
    2. Boswijk, H. Peter & Laeven, Roger J.A. & Vladimirov, Evgenii, 2024. "Estimating option pricing models using a characteristic function-based linear state space representation," Journal of Econometrics, Elsevier, vol. 244(1).
    3. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    4. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
    5. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    6. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.
    7. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    8. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    9. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    10. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    11. Algieri, Bernardina & Leccadito, Arturo & Tunaru, Diana, 2021. "Risk premia in electricity derivatives markets," Energy Economics, Elsevier, vol. 100(C).
    12. Byun, Suk Joon & Jeon, Byoung Hyun & Min, Byungsun & Yoon, Sun-Joong, 2015. "The role of the variance premium in Jump-GARCH option pricing models," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 38-56.
    13. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    14. Bingxin Li, 2020. "Option-implied filtering: evidence from the GARCH option pricing model," Review of Quantitative Finance and Accounting, Springer, vol. 54(3), pages 1037-1057, April.
    15. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    16. Adam Aleksander Majewski & Giacomo Bormetti & Fulvio Corsi, 2014. "Smile from the Past: A general option pricing framework with multiple volatility and leverage components," Papers 1404.3555, arXiv.org.
    17. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    18. Hsuan‐Ling Chang & Yen‐Cheng Chang & Hung‐Wen Cheng & Po‐Hsiang Peng & Kevin Tseng, 2019. "Jump variance risk: Evidence from option valuation and stock returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(7), pages 890-915, July.
    19. Robert Azencott & Yutheeka Gadhyan & Roland Glowinski, 2014. "Option Pricing Accuracy for Estimated Heston Models," Papers 1404.4014, arXiv.org, revised Jul 2015.
    20. Neumann, Maximilian & Prokopczuk, Marcel & Wese Simen, Chardin, 2016. "Jump and variance risk premia in the S&P 500," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 72-83.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2511.14980. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.