Statistical Modelling 9 (2009), 69–95
Stochastic volatility models for ordinal-valued time series with application to finance
Gernot Müller
Zentrum Mathematik,
Technische Universität München,
Boltzmannstraße 3,
D–85747 München
Germany
eMail:
mueller@ma.tum.de
Claudia Czado
Zentrum Mathematik,
Technische Universität München,
Boltzmannstraße 3,
D–85747 München
Germany
eMail:
cczado@ma.tum.de
Abstract:
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.
Keywords:
grouped move; high-frequency finance; Markov chain Monte Carlo;
multigrid Monte Carlo; price process; transformation group
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