Estimation of the Probability of Informed Trading Models Via an Expectation-Conditional Maximization Algorithm

Abstract

The PIN model and its extensions have proven challenging in their estimation, as they suffer from several computational problems. We set in this paper to address these computational issues by proposing the use of the expectation-conditional maximization (ECM) algorithm to estimate the various models of probability of informed trading. In particular, we derive optimal estimates of two of the extensions of the original PIN model, which are the MPIN model as introduced by Ersan (2016), and the adjusted PIN of Duarte and Young (2009)), as well as its restricted variants. The derivation provides a reliable and mathematically sound method for the estimation of the number of information layers for the MPIN model, as well as, stable estimates for the adjusted PIN model despite the large number of free variables. We show that the maximum likelihood estimation via the ECM algorithm is faster, and more reliable, and provides a viable alternative to the standard methods used in the literature. In addition to providing more accurate estimates of probability parameters, the ECM algorithm allows for an endogenous determination of the number of layers in the MPIN model. This paper has served as the basis of the implementation of the ECM estimation in the R package dedicated to the estimation of probability of informed trading models: PINstimation.

Keywords: Multilayer probability of informed trading, MPIN, adjusted PIN model, expectation conditional maximization, information asymmetry, private information

JEL Classification: C13, C38, G14, G17