We propose a novel extension of the score-driven POT (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. In 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.