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Nonparametric Bayesian Volatility Estimation

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2017 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 2))

Abstract

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time interval. The values on the bins are assigned an inverse Gamma Markov chain (IGMC) prior. Posterior inference is straightforward to implement via Gibbs sampling, as the full conditional distributions are available explicitly and turn out to be inverse Gamma. We also discuss in detail the hyperparameter selection for our method. Our nonparametric Bayesian approach leads to good practical results in representative simulation examples. Finally, we apply it on a classical data set in change-point analysis: weekly closings of the Dow-Jones industrial averages.

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Acknowledgements

The research leading to the results in this paper has received funding from the European Research Council under ERC Grant Agreement 320637.

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Authors and Affiliations

  1. Mathematical Institute, Leiden University, Leiden, The Netherlands

    Shota Gugushvili & Moritz Schauer

  2. Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands

    Frank van der Meulen

  3. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    Peter Spreij

  4. Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands

    Peter Spreij

Authors
  1. Shota Gugushvili
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  2. Frank van der Meulen
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  3. Moritz Schauer
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  4. Peter Spreij
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Correspondence to Peter Spreij .

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Editors and Affiliations

  1. The University of Melbourne, Melbourne, Australia

    Jan de Gier

  2. University of Western Australia, Perth, Australia

    Cheryl E. Praeger

  3. UCLA, Los Angeles, CA, USA

    Terence Tao

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Gugushvili, S., der Meulen, F.v., Schauer, M., Spreij, P. (2019). Nonparametric Bayesian Volatility Estimation. In: de Gier, J., Praeger, C., Tao, T. (eds) 2017 MATRIX Annals. MATRIX Book Series, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-030-04161-8_19

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