The sequence of instantaneous driving decisions and its variations, known as driving volatility, prior to involvement in safety critical events can be a leading indicator of safety. Here, this study focuses on the component of ?driving volatility matrix? related to specific normal and safety-critical events, named ?event-based volatility.? The research issue is characterizing volatility in instantaneous driving decisions in the longitudinal and lateral directions, and how it varies across drivers involved in normal driving, crash, and/or near-crash events. To explore the issue, a rigorous quasi-experimental study design is adopted to help compare driving behaviors in normal vs unsafe outcomes. Using a unique real-world naturalistic driving database from the 2nd Strategic Highway Research Program (SHRP), a test set of 9593 driving events featuring 2.2 million temporal samples of real-world driving are analyzed. This study features a plethora of kinematic sensors, video, and radar spatiotemporal data about vehicle movement and therefore offers the opportunity to initiate such exploration. By using information related to longitudinal and lateral accelerations and vehicular jerk, 24 different aggregate and segmented measures of driving volatility are proposed that captures variations in extreme instantaneous driving decisions. In doing so, careful attention is given to the issue of intentional vs. unintentional volatility. The volatility indices, as leading indicators of near-crash and crash events, are then linked with safety critical events, crash propensity, and other event specific explanatory variables. Owing to the presence of unobserved heterogeneity and omitted variable bias, fixed- and random-parameter discrete choice models are developed that relate crash propensity to unintentional driving volatility and other factors. Statistically significant evidence is found that driver volatilities in near-crash and crash events are significantly greater than volatility in normal driving events. After controlling for traffic, roadway, and unobserved factors, the results suggest that greater intentional volatility increases the likelihood of both crash and near-crash events. A one-unit increase in intentional volatility is associated with positive vehicular jerk in longitudinal direction increases the chance of crash and near-crash outcome by 15.79 and 12.52 percentage points, respectively. Importantly, intentional volatility in positive vehicular jerk in lateral direction has more negative consequences than intentional volatility in positive vehicular jerk in longitudinal direction. Compared to acceleration/deceleration, vehicular jerk can better characterize the volatility in microscopic instantaneous driving decisions prior to involvement in safety critical events. Finally, the magnitudes of correlations exhibit significant heterogeneity, and that accounting for the heterogeneous effects in the modeling framework can provide more reliable and accurate results. The study demonstrates the value of quasi-experimental study design and big data analytics for understanding extreme driving behaviors in safe vs. unsafe driving outcomes.