A micro-movement model with Bayes estimation via filtering: Application to measuring trading noises and costs

We highlight a general hybrid system as the micromovement model for asset price using counting processes recently introduced with its Bayes estimation via filtering. We construct a new simple micromovement model and apply it to analyze trade-by-trade stock price data in the light of the series of works initiated by Christie and Schultz [Why do NASDAQ market makers avoid odd-eighth quotes?, Finance 49 (1994) 1813–1840]. Through the new model, we propose more reasonable, but computationally intensive measures for trading noise including clustering noise and non-clustering noise, and for trading cost. We employ Bayes estimation via filtering to obtain parameter estimates of the new model and to provide numerical measures of trading noise and trading cost for three stocks from four chosen periods. Our empirical results support the important findings in [Christie, Harris, Schultz, Why did NASDAQ market makers stop avoiding odd-eighth quotes?, Finance 49 (1994) 1841–1860; Barclay, Christie, Harris, Kandel, Schultz, The effects of market reform on the trading costs and depths of NASDAQ stocks, J. Finance 54(1) (1999) 1–34].