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

See all articles by Kam Hamidieh

Kam Hamidieh

University of Pennsylvania; Statistics and Data Sciences

Stilian Stoev

Boston University - Department of Mathematics and Statistics

George Michailidis

University of Michigan at Ann Arbor

Date Written: January 11, 2012

Abstract

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

Suggested Citation

Hamidieh, Kamal and Stoev, Stilian and Michailidis, George, Intensity Based Estimation of Extreme Loss Event Probability and Value-at-Risk (January 11, 2012). Applied Stochastic Models in Business and Industry, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1107538 or http://dx.doi.org/10.2139/ssrn.1107538

Kamal Hamidieh (Contact Author)

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

Statistics and Data Sciences ( email )

2317 Speedway
Austin, TX 78712
United States

Stilian Stoev

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

George Michailidis

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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