In this paper, we introduce a new class of models, called ordinal-response stochastic volatility 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 coarse grid. 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 samples of a certain conditional distribution. Also volatility estimates are provided. For illustration, we apply our new model class to price changes of the IBM stock. Dependencies on covariates are quantified and compared with theoretical results for such processes.