IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00338114.html
   My bibliography  Save this paper

Calibration of local volatility using the local and implied instantaneous variance

Author

Listed:
  • Gabriel Turinici

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a Gauss-Newton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) approach. The procedure performs well on benchmarks from the literature and on FOREX data.

Suggested Citation

  • Gabriel Turinici, 2009. "Calibration of local volatility using the local and implied instantaneous variance," Post-Print hal-00338114, HAL.
    • Handle: RePEc:hal:journl:hal-00338114
    Note: View the original document on HAL open archive server: https://hal.science/hal-00338114v2
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00338114v2/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
    2. Thomas F. Coleman & Yuying Li & Arun Verma, 2001. "Reconstructing The Unknown Local Volatility Function," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 7, pages 192-215, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gabriel Turinici, 2009. "Robust recovery of the risk neutral probability density from option prices," Analele Stiintifice ale Universitatii "Alexandru Ioan Cuza" din Iasi - Stiinte Economice (1954-2015), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 56, pages 197-201, November.
    2. F. Gerlich & A. Giese & J. Maruhn & E. Sachs, 2012. "Parameter identification in financial market models with a feasible point SQP algorithm," Computational Optimization and Applications, Springer, vol. 51(3), pages 1137-1161, April.
    3. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.

    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. Gabriel TURINICI, 2008. "Local Volatility Calibration Using An Adjoint Proxy," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 2, pages 93-105, November.
    2. Yishen Li & Jin Zhang, 2004. "Option pricing with Weyl-Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 457-464.
    3. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    4. Zui-Cha Deng & Y.-C. Hon & Liu Yang, 2014. "An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 890-910, March.
    5. Xu, Wei & Šević, Aleksandar & Šević, Željko, 2022. "Implied volatility surface construction for commodity futures options traded in China," Research in International Business and Finance, Elsevier, vol. 61(C).
    6. Deng, Zui-Cha & Yu, Jian-Ning & Yang, Liu, 2008. "Identifying the coefficient of first-order in parabolic equation from final measurement data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 421-435.
    7. David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 197-206.
    8. Liang, J. & Gao, Y., 2012. "Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives," Economic Modelling, Elsevier, vol. 29(4), pages 1278-1285.
    9. S. Gnanavel & N. Barani Balan & K. Balachandran, 2014. "Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 992-1008, March.
    10. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2023. "Data-driven Approach for Static Hedging of Exchange Traded Options," Papers 2302.00728, arXiv.org, revised Jan 2024.
    11. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    12. Min Dai & Hanqing Jin & Xi Yang, 2024. "Data-driven Option Pricing," Papers 2401.11158, arXiv.org.
    13. Judith Glaser & Pascal Heider, 2012. "Arbitrage-free approximation of call price surfaces and input data risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 61-73, August.
    14. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
    15. Dai, Min & Tang, Ling & Yue, Xingye, 2016. "Calibration of stochastic volatility models: A Tikhonov regularization approach," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 66-81.

    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:hal:journl:hal-00338114. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.