  The price clustering phenomenon manifesting itself as an increased occurrence
of specific prices is widely observed and well-documented for various financial
instruments and markets. In the literature, however, it is rarely incorporated
into price models. We consider that there are several types of agents trading
only in specific multiples of the tick size resulting in an increased
occurrence of these multiples in prices. For example, stocks on the NYSE and
NASDAQ exchanges are traded with precision to one cent but multiples of five
cents and ten cents occur much more often in prices. To capture this behavior,
we propose a discrete price model based on a mixture of double Poisson
distributions with dynamic volatility and dynamic proportions of agent types.
The model is estimated by the maximum likelihood method. In an empirical study
of DJIA stocks, we find that higher instantaneous volatility leads to weaker
price clustering at the ultra-high frequency. This is in sharp contrast with
results at low frequencies which show that daily realized volatility has a
positive impact on price clustering.
