Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
Statistics Theory
2023-10-18 v2 Methodology
Statistics Theory
Abstract
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 (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.
Cite
@article{arxiv.2011.08321,
title = {Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations},
author = {Denis Belomestny and Shota Gugushvili and Moritz Schauer and Peter Spreij},
journal= {arXiv preprint arXiv:2011.08321},
year = {2023}
}