Stochastic volatility models for ordinal valued time series with application to finance

In this paper we introduce two stochastic volatility models where
the response variable takes on only finite many ordered values.
Corresponding time series occur in high-frequency finance when the
stocks are traded on a coarse grid. For parameter estimation we
develop an e±cient Grouped Move Multigrid Monte Carlo (GM-MGMC)
sampler. We apply both models to price changes of the IBM stock in
January, 2001 at the NYSE. Dependencies of the price change process
on covariates are quantified and compared with theoretical
considerations on such processes. We also investigate whether this
data set requires modeling with a heavy-tailed Student-t
distribution.