Probability of Informed No-Tradings: A Copula-Based PIN Model with Zero-Inflated Poisson Distributions

¹ Institue of Statistics, National Yang Ming Chiao-Tung University, Taiwan
² Department of Fashion Administration and Management, St. John’s University, Taiwan
³ Institute of Statistical Science, Academia Sinica, Taiwan

^* e-mail: chulankao@gmail.com
^** e-mail: mlin@mail.sju.edu.tw
^*** e-mail: 594537@gmail.com

Abstract

Classical probability of informed trading (PIN) models assume that, given the information scenario, the number of buy and sell order flows are independently Poisson distributed, which imposes an assumption on the probability of no-trades. However, empirical data shows that the implied probabilities of no-trades do not match the aforementioned Poisson and independent assumptions. Therefore, we propose a new PIN model that better fits the data by using zero-inflated Poisson distributions and copula functions, which allow us to match the probability of no-trades. The expectation conditional maximization (ECM) is further proposed to tackle the parameter fittings, which is verified by simulation studies. The empirical studies show that this model outperforms the original PIN models, with significant parameters on the zero-inflations as well as copulas. In particular, we find that it is possible for an information to simultaneously increase the probability of no trade and boost up the average number of transactions, which contradicts the intuition.