Forecasting Extreme Returns in Financial Markets: A Discrete Duration Framework

K. Bień-Barkowska Institute of Econometrics, Warsaw School of Economics, Madalińskiego 6/8, 02-513 Warsaw, Poland

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We introduce a new dynamic peaks-over-threshold (POT) model for predicting both the timing and the size of extreme losses in financial markets. The novelty of our approach lies in treating the times at which the magnitude of loss exceeds a sufficiently large threshold as a realization of a discrete random variable. The conditional hazard function with respect to the time in-between consecutive extreme losses - and hence, the risk of an extreme loss over the next time unit - is described using two lifetime distributions: the discrete Weibull and the discrete Burr. To consider the clustering of extreme losses, the scale parameters of these discrete distributions vary with time and have the functional form of autoregressive conditional duration (ACD) models. Accordingly, the probability of an extreme loss over the next unit of time depends on times of extreme losses in the past and the period that has elapsed since the last such event. We demonstrate how to predict the value at risk (VaR) from the discrete-duration POT model and empirically confirm that this new approach provides a good alternative to the ACD-POT models outlined in the literature.

DOI:10.12693/APhysPolA.138.48 topics: extreme losses, peaks-over-threshold (POT) model, ACD models, discrete durations