Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
Journal article, 2022
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward procedure for posterior inference via an MCMC procedure. We give theoretical performance guarantees (minimax optimal contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.
nonparametric Bayesian estimation
Gamma process
stochastic differential equation
Author
Denis Belomestny
University of Duisburg-Essen
National Research University Higher School of Economics
Shota Gugushvili
Wageningen University and Research
Moritz Schauer
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Peter Spreij
Korteweg-de Vries Institute for Mathematics
Radboud University
Bernoulli
1350-7265 (ISSN)
Vol. 28 4 2151-2180Subject Categories
Computational Mathematics
Probability Theory and Statistics
Mathematical Analysis
DOI
10.3150/21-BEJ1413