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Testing the local volatility assumption: a statistical approach

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Author Info

  • 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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File URL: http://hdl.handle.net/10.1007/s10436-011-0180-z
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Bibliographic Info

Article provided by Springer in its journal Annals of Finance.

Volume (Year): 8 (2012)
Issue (Month): 1 (February)
Pages: 31-48

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Handle: RePEc:kap:annfin:v:8:y:2012:i:1:p:31-48

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Web page: http://www.springerlink.com/link.asp?id=112370

Related research

Keywords: Local volatility models; Stochastic volatility models; Test statistics; Semi-martingales; Limit theorems; 60F05; 60G44; 60J60; 62M02; 62M07;

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References

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  1. Ole Barndorff-Nielsen & Svend Erik Graversen & Jean Jacod & Mark Podolskij & Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Papers 2004-W29, Economics Group, Nuffield College, University of Oxford.
  2. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre.
  3. Vetter, Mathias & Podolskij, Mark & Dette, Holger, 2004. "Estimation of integrated volatility in continuous time financial models with applications to goodness-of-fit testing," Technical Reports 2004,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  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. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
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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, School of Economics and Management, University of Aarhus.

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