IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v20y2017i01ns0219024917500066.html
   My bibliography  Save this article

Convex Regularization Of Local Volatility Estimation

Author

Listed:
  • VINICIUS ALBANI

    (Department of Mathematics, Federal University of Santa Catarina, Trindade, Florianopolis, Santa Catarina 88.040-900, Brazil)

  • ADRIANO DE CEZARO

    (Institute of Mathematics, Statistics and Physics, Federal University of Rio Grande, Av. Italia Km 8, Rio Grande, Rio Grande do Sul 96201-900, Brazil)

  • JORGE P. ZUBELLI

    (Instituto of Pure and Applied Mathematics, Estrada Dona Castorina, 110, Jardim Botnico, Rio de Janeiro, Rio de Janeiro 22460-320, Brazil)

Abstract

We apply convex regularization techniques to the problem of calibrating Dupire’s local volatility surface model taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far away from the at-the-money level. We obtain convergence rates and results comparable to those obtained in the idealized continuous setting. Our results allow us to take into account separately the uncertainties due to the price noise and those due to discretization errors, thus, allowing estimating better discretization levels both in the domain and in the image of the parameter to solution operator by a Morozov’s discrepancy principle. We illustrate the results with simulated as well as real market data. We also validate the results by comparing the implied volatility prices of market data with the computed prices of the calibrated model.

Suggested Citation

  • Vinicius Albani & Adriano De Cezaro & Jorge P. Zubelli, 2017. "Convex Regularization Of Local Volatility Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-37, February.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500066
    DOI: 10.1142/S0219024917500066
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024917500066
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024917500066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marco Avellaneda, 1998. "Minimum-Relative-Entropy Calibration of Asset-Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 447-472.
    2. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    3. Roger W. Lee, 2001. "Implied And Local Volatilities Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 45-89.
    4. Marco Avellaneda & Robert Buff & Craig Friedman & Nicolas Grandechamp & Lukasz Kruk & Joshua Newman, 2001. "Weighted Monte Carlo: A New Technique For Calibrating Asset-Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 91-119.
    5. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    6. Marco Avellaneda & Robert Buff & Craig Friedman & Nicolas Grandechamp & Lukasz Kruk & Joshua Newman, 2001. "Weighted Monte Carlo: A New Technique For Calibrating Asset-Pricing Models," 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 9, pages 239-265, 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. Jorge P. Zubelli & Kuldeep Singh & Vinicius Albani & Ioannis Kourakis, 2024. "Travelling wave solutions of an equation of Harry Dym type arising in the Black-Scholes framework," Papers 2412.19020, arXiv.org.
    2. Soobin Kwak & Youngjin Hwang & Yongho Choi & Jian Wang & Sangkwon Kim & Junseok Kim, 2022. "Reconstructing the Local Volatility Surface from Market Option Prices," Mathematics, MDPI, vol. 10(14), pages 1-12, July.
    3. Yuri F. Saporito & Xu Yang & Jorge P. Zubelli, 2017. "The Calibration of Stochastic-Local Volatility Models - An Inverse Problem Perspective," Papers 1711.03023, arXiv.org.
    4. Vinicius V. L. Albani & Jorge P. Zubelli, 2020. "A splitting strategy for the calibration of jump-diffusion models," Finance and Stochastics, Springer, vol. 24(3), pages 677-722, July.

    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. José L. Vilar-Zanón & Olivia Peraita-Ezcurra, 2019. "A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 259-276, June.
    2. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.
    3. Hadrien De March & Pierre Henry-Labordere, 2019. "Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants," Papers 1902.04456, arXiv.org, revised Jul 2023.
    4. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
    5. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Papers 1904.04554, arXiv.org.
    6. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    7. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Working Papers hal-02090807, HAL.
    8. Hadrien de March & Pierre Henry-Labordere, 2019. "Building Arbitrage-Free Implied Volatility: Sinkhorn'S Algorithm And Variants," Working Papers hal-02011533, HAL.
    9. Andre Catalao & Rogerio Rosenfeld, 2018. "Analytical Path-Integral Pricing of Moving-Barrier Options under non-Gaussian Distributions," Papers 1804.07852, arXiv.org.
    10. André Catalão & Rogério Rosenfeld, 2020. "Analytical Path-Integral Pricing Of Deterministic Moving-Barrier Options Under Non-Gaussian Distributions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-52, February.
    11. Yanchu Liu & Chen Liu & Yiyao Chen & Xianming Sun, 2024. "Option‐Implied Ambiguity and Equity Return Predictability," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(9), pages 1556-1577, September.
    12. Stephane Crepey, 2004. "Delta-hedging vega risk?," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 559-579.
    13. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    14. José L. Vilar-Zanón & Barbara Rogo, 2024. "Pricing and Hedging Contingent Claims by Entropy Segmentation and Fenchel Duality," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-20, December.
    15. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2022. "ESG-Valued Portfolio Optimization and Dynamic Asset Pricing," Papers 2206.02854, arXiv.org.
    16. Rama Cont, 2023. "In memoriam: Marco Avellaneda (1955–2022)," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 3-15, January.
    17. Lelièvre, Tony & Samaey, Giovanni & Zieliński, Przemysław, 2020. "Analysis of a micro–macro acceleration method with minimum relative entropy moment matching," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3753-3801.
    18. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.
    19. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    20. Jim Gatheral, 2023. "Marco Avellaneda: Mathematician and trader," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 16-18, January.

    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:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500066. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.