Nonparametric Bayesian volatility learning under microstructure noise

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

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Abstract: 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 \emph{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.

Date: 2018-05, Revised 2024-03
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Published in Jpn. J. Stat. Data. Sci 6, 551-571 (2023)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1805.05606

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