Stochastic volatility models for ordinal-valued timeseries with application to finance

摘要

In this paper, we introduce a new class of models, called ordinal-response stochasticvolatility models, by combining an ordinal-response model and the idea of stochastic volatility.Corresponding time series occur in high-frequency finance when the stocks are traded on a coarsegrid. For parameter estimation, we develop an efficient grouped move multigrid Monte Carlo sampler.This sampler is based on a scale transformation group, whose elements operate on the random samplesof a certain conditional distribution. Also volatility estimates are provided. For illustration, we applyour new model class to price changes of the IBM stock. Dependencies on covariates are quantified andcompared with theoretical results for such processes.