Nonparametric Bayesian volatility learning under microstructure noise

Shota Gugushvili, Frank van der Meulen*, Moritz Schauer, Peter Spreij

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesian approach, where we a priori model the volatility function as piecewise constant. Its prior is specified via the inverse Gamma Markov chain. Sampling from the posterior is accomplished by incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs sampler. Good performance of the method is demonstrated on two representative synthetic data examples. We also apply the method on a EUR/USD exchange rate dataset. Finally we present a limit result on the prior distribution.

Original languageEnglish
Pages (from-to)551-571
Number of pages21
JournalJapanese Journal of Statistics and Data Science
Issue number1
Publication statusPublished - 2022
Externally publishedYes


  • Forward Filtering Backward Simulation
  • Gibbs sampler
  • High frequency data
  • Inverse Gamma Markov chain
  • Microstructure noise
  • State-space model
  • Volatility


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