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Model Selection for Volatility Prediction

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The Fascination of Probability, Statistics and their Applications

Abstract

We consider a stochastic regression model defined by stochastic differential equations. Based on an expected Kullback-Leibler information for the approximated distributions, we propose an information criterion for selection of volatility models. We show that the information criterion is asymptotically unbiased for the expected Kullback-Leibler information. We also give examples and simulation results of model selection.

Dedicated to Professor Ole Barndorff-Nielsen on the occasion of his 80th birthday

This work was in part supported by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Nos. 24340015 and 24300107 (Scientific Research), Nos. 24654024, 24650148 and 26540011 (Challenging Exploratory Research); CREST Japan Science and Technology Agency; NS Solutions Corporation; and by a Cooperative Research Program of the Institute of Statistical Mathematics. The authors thank the referee for valuable comments.

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Notes

  1. 1.

    However, as a matter of fact, it is incorrect as for estimation of volatility.

  2. 2.

    That is, there exists a constant C such that \(|\partial _\theta ^\mathbf{\nu } \partial _x^\mathbf{n} f(x,\theta )| \le C(1+|x|)^C\) for all \((x,\theta )\in {\mathbb R}^\mathsf{d}\times \Theta \).

  3. 3.

    The integrability condition can be relaxed, in fact.

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Author information

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Osaka, Japan

    Masayuki Uchida

  2. Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, Japan

    Nakahiro Yoshida

  3. CREST, Japan Science and Technology Agency, Tokyo, Japan

    Masayuki Uchida & Nakahiro Yoshida

Authors
  1. Masayuki Uchida
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  2. Nakahiro Yoshida
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Correspondence to Nakahiro Yoshida .

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Editors and Affiliations

  1. Department of Mathematics, University of Aarhus, Aarhus, Denmark

    Mark Podolskij

  2. Institute of Mathematical Finance, Ulm University, Ulm, Germany

    Robert Stelzer

  3. Department of Mathematics, University of Aarhus, Aarhus C, Denmark

    Steen Thorbjørnsen

  4. Department of Mathematics Huxley Building, Room 551, Imperial College London, London, United Kingdom

    Almut E. D. Veraart

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Uchida, M., Yoshida, N. (2016). Model Selection for Volatility Prediction. In: Podolskij, M., Stelzer, R., Thorbjørnsen, S., Veraart, A. (eds) The Fascination of Probability, Statistics and their Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-25826-3_16

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