A New Way to Compute the Probability of Informed Trading

Volume-Synchronized Probability of Informed Trading (VPIN) is a tool designed to predict extreme events like flash crashes in high-frequency trading. Its aim is to estimate the Probability of Informed Trading (PIN), which was built from a probabilistic framework. Some concerns have been raised about its theoretical foundations and its reliability. More precisely, it has been shown that theoretically the VPIN does not approximate the PIN as the PIN has been built with a time-clock framework and the VPIN with a volume clock one. On a practical point of view, the VPIN has been found to be sensitive to the starting point of computation of a data set and to different parameters, such as the classification rule. In this paper, in order to improve the PIN theoretical framework, we firstly analyze the theoretical foundations of the PIN and the VPIN models to have a better view of all its different assumption subtleties. It secondly makes it possible to point out some approximation flaws in the formula used to approximate the PIN and to propose another exact way to compute the PIN. All different results are illustrated with simulations.