A Faster Estimation Method for the Probability of Informed Trading Using Hierarchical Agglomerative Clustering

Abstract

The probability of informed trading (PIN) is a commonly used market microstructure measure for detecting the level of information asymmetry. Estimating PIN can be problematic due to corner solutions, local maxima and floating point exceptions (FPE). Yan and Zhang (2012) show that whilst factorization can solve FPE, boundary solutions appear frequently in maximum likelihood estimation for PIN. A grid search initial value algorithm is suggested to overcome this problem. We present a faster method for reducing the likelihood of boundary solutions and local maxima based on hierarchical agglomerative clustering (HAC). We show that HAC can be used to determine an accurate and fast starting value approximation for PIN. This assists the maximum likelihood estimation process in both speed and accuracy.

Keywords: PIN, CPIN, Market microstructure, Cluster analysis, Mixture model, Skellam distribution

JEL Classification: C13, C38, C46, D53, G10, G12, G14