A method to overcome the numerical difficulties in PIN estimation

The Probability of Information (PIN)-based trading introduced by Easley et al. (1996, 2002) has been adopted to address a variety of issues in empirical finance. To obtain PIN using numerical Maximum Likelihood Estimation (MLE) from transaction data, one may suffer from the numerical overflow or underflow problems which are more pronounced for active stocks than for inactive stocks. As buy and sell orders increase, more and more stocks fall into the category for which the PIN estimation simply falls. Based on the round-off error in digital computing, this article proposes a recipe to eradicate such numerical difficulties, which sheds light on heavily traded stocks.