Intensity Based Estimation of Extreme Loss Event Probability and Value-at-Risk
Applied Stochastic Models in Business and Industry, Forthcoming
28 Pages Posted: 25 Mar 2008 Last revised: 6 Apr 2015
Date Written: January 11, 2012
We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self-exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability.
Keywords: Point Processes, Clustering, Autoregressive Conditional Duration, Extreme Risk, Generalized Pareto Distribution
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