2018/01/31 by Shota Gugushvili, Frank van der Meulen, Moritz Schauer +1 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Financial Risk and Volatility Modeling #Gibbs sampling #Markov chain #Markov chain Monte Carlo #Nonparametric statistics #Statistical Methods and Inference #Stochastic volatility #Volatility (finance) #math.ST #msc:62G20 #msc:62M05 #q-fin.ST #stat.ME #stat.TH
paper · pdf · doi:10.1007/978-3-030-04161-8_19
published in MATRIX book series, 279-302 (Springer International Publishing)
openalex created_date 2018/02/23 · openalex publication_date 2019/01/01 · arxiv created 2019/03/29 · arxiv updated 2019/04/01 · openalex updated_date 2026/08/05
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.