Modeling price clustering in high-frequency prices
提出一个混合双泊松分布模型，捕捉高频价格中特定价格倍数出现更频繁的现象，并发现瞬时波动率越高，超高频价格聚类越弱，与低频结果相反。
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.