Abstract

This study provides a theoretical basis for the transformation of the probability of informed trading model to the volume-synchronized probability of informed trading (VPIN) setting based on volume buckets. Building on Easley et al. (2011, 2012b), who derive the VPIN metric and provide evidence of its usefulness, we expand the analytical basis of the model and clarify its derivation. We show mathematically that Easley et al.’s VPIN metric becomes unstable for small volume buckets and for infrequent informed trades. In contrast, we use a maximum likelihood estimation to capture the information in volume time, and as a result our improved VPIN mathematical model generates consistent estimates. We also show that the volume time measure helps improve the predictability of VPIN for the flow toxicity.