Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time interval. The values on the bins are assigned an inverse Gamma Markov chain (IGMC) prior. Posterior inference is straightforward to implement via Gibbs sampling, as the full conditional distributions are available explicitly and turn out to be inverse Gamma. We also discuss in detail the hyperparameter selection for our method. Our nonparametric Bayesian approach leads to good practical results in representative simulation examples. Finally, we apply it on a classical data set in change-point analysis: weekly closings of the Dow-Jones industrial averages.
Original languageEnglish
Title of host publication2017 MATRIX Annals
EditorsD. Wood, J. de Gier, C. Praeger, T. Tao
Place of PublicationCham
PublisherSpringer
Pages279-302
Number of pages24
ISBN (Electronic)978-3-030-04161-8
ISBN (Print)978-3-030-04160-1
DOIs
Publication statusPublished - 2019

Publication series

NameMATRIX Book Series book series
Volume2

ID: 67209698