Nonparametric Bayesian Volatility Estimation

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


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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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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematical InstituteLeiden UniversityLeidenThe Netherlands
  2. 2.Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands
  3. 3.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.Institute for Mathematics, Astrophysics and Particle PhysicsRadboud UniversityNijmegenThe Netherlands

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