When to be discrete: The importance of time formulation in the modeling of extreme events in finance

Abstract

We propose a novel extension of the score-driven peaks-over-threshold (SPOT) model within a discrete-time framework. This adaptation is motivated by the fact that financial returns and, consequently, extreme events are typically observed at discrete time intervals. Our primary objective is to assess whether this discrete-time SPOT model provides a more precise representation and superior fit for tail risk forecasting. The study reveals several important findings. First, we demonstrate that continuous-time approaches can result in inaccurate value-at-risk and expected-shortfall forecasts. By contrast, discrete-time models provide a more accurate description of the dynamics of extreme losses. Empirical evidence supports the superiority of discrete-duration models, outperforming various continuous-time SPOT specifications and GARCH models. Overall, our study has substantial implications for the modeling and forecasting of extreme financial events, offering a more accurate and efficient approach than traditional approaches.