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Testing the local volatility assumption: a statistical approach

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  • Mark Podolskij
  • Mathieu Rosenbaum

Abstract

In practice, the choice of using a local volatility model or a stochastic volatility model is made according to their respective ability to fit implied volatility surfaces. In this paper, we adopt an opposite point of view. Indeed, based on historical data, we design a statistical procedure aiming at testing the assumption of a local volatility model for the price dynamics, against the alternative of a stochastic volatility model.
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Suggested Citation

  • Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
    • Handle: RePEc:kap:annfin:v:8:y:2012:i:1:p:31-48
    DOI: 10.1007/s10436-011-0180-z
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    References listed on IDEAS

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    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    2. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
    4. Dette, Holger & Podolskij, Mark, 2005. "Testing the parametric form of the volatility in continuous time diffusion models: an empirical process approach," Technical Reports 2005,50, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278, June.
    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.
    7. A. Alvarez & F. Panloup & M. Pontier & N. Savy, 2008. "Estimation of the instantaneous volatility," Papers 0812.3538, arXiv.org, revised Sep 2010.
    8. Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.
    9. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
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    Citations

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    Cited by:

    1. Jean Jacod & Mark Podolskij, 2012. "A Test for the Rank of the Volatility Process: The Random Perturbation Approach," Global COE Hi-Stat Discussion Paper Series gd12-268, Institute of Economic Research, Hitotsubashi University.
    2. Jean Jacod & Mark Podolskij, 2012. "A test for the rank of the volatility process: the random perturbation approach," CREATES Research Papers 2012-57, Department of Economics and Business Economics, Aarhus University.
    3. Melnykova, Anna & Reynaud-Bouret, Patricia & Samson, Adeline, 2024. "Non-asymptotic statistical tests of the diffusion coefficient of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    4. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02383135, HAL.
    5. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Post-Print halshs-02383135, HAL.

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    More about this item

    Keywords

    Local volatility models; Stochastic volatility models; Test statistics; Semi-martingales; Limit theorems; 60F05; 60G44; 60J60; 62M02; 62M07;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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