Nonparametric Bayesian volatility learning under microstructure noise
Journal article, 2023

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.

State-space model

Inverse Gamma Markov chain

Microstructure noise

High frequency data

Gibbs sampler

Volatility

Forward Filtering Backward Simulation

Author

Shota Gugushvili

Wageningen University and Research

Frank van der Meulen

Vrije Universiteit Amsterdam

Moritz Schauer

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Peter Spreij

University of Amsterdam

Radboud University

Japanese Journal of Statistics and Data Science

25208764 (eISSN)

Vol. 6 1 551-571

Subject Categories

Probability Theory and Statistics

DOI

10.1007/s42081-022-00185-9

More information

Latest update

7/5/2023 1