Forecasting extreme negative returns in gold and silver: A discrete‐duration approach to POT models

Abstract

Sudden and massive drops in precious metal prices severely impact the investment risk on these commodity markets. In this study, we examine the dynamics of extreme negative returns on gold and silver, as well as propose the discrete‐duration version of the autoregressive conditional duration peaks‐over‐threshold (ACD‐POT) model for measuring market risk. The model is tailored for the dynamics of extreme events in precious metal markets; this is because it can exhibit both the strong clustering of extreme‐event days, and the serial correlation in the magnitudes of extreme losses. From an econometric perspective, our approach complements the existing dynamic versions of POT models; this is so that the time interval (i.e., duration) between the extreme negative returns is treated not as a continuous variable, but as a discrete one. The discrete hazard function in our model represents the daily extreme loss event probability and it can be used to derive one‐day‐ahead forecasts of both the value at risk and expected shortfall for investments in gold and silver. Formal backtesting methods show that the discretized version of the POT model has a superior in‐sample fit and forecasting performance than the continuous‐duration POT models.