Multivariate Dynamic Intensity Peaks-Over-Threshold Models

CFS Working Paper No. 516

43 Pages Posted: 22 Sep 2015

See all articles by Nikolaus Hautsch

Nikolaus Hautsch

University of Vienna - Department of Statistics and Operations Research; Center for Financial Studies (CFS)

Rodrigo Herrera

University of Talca

Date Written: September 16, 2015

Abstract

We propose a multivariate dynamic intensity peaks-over-threshold model to capture extreme events in a multivariate time series of returns. The random occurrence of extreme events exceeding a threshold is modeled by means of a multivariate dynamic intensity model allowing for feedback effects between the individual processes. We propose alternative specifications of the multivariate intensity process using autoregressive conditional intensity and Hawkes-type specifications. Likewise, temporal clustering of the size of exceedances is captured by an autoregressive multiplicative error model based on a generalized Pareto distribution. We allow for spillovers between both the intensity processes and the process of marks. The model is applied to jointly model extreme returns in the daily returns of three major stock indexes. We find strong empirical support for a temporal clustering of both the occurrence of extremes and the size of exceedances. Moreover, significant feedback effects between both types of processes are observed. Backtesting Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts show that the proposed model does not only produce a good in-sample fit but also reliable out-of-sample predictions. We show that the inclusion of temporal clustering of the size of exceedances and feedback with the intensity thereof results in better forecasts of VaR and ES.

Keywords: Extreme value theory, Value-at-Risk, Expected shortfall, Self-exciting point process, Conditional intensity

Suggested Citation

Hautsch, Nikolaus and Herrera, Rodrigo, Multivariate Dynamic Intensity Peaks-Over-Threshold Models (September 16, 2015). CFS Working Paper No. 516. Available at SSRN: https://ssrn.com/abstract=2663353 or http://dx.doi.org/10.2139/ssrn.2663353

Nikolaus Hautsch (Contact Author)

University of Vienna - Department of Statistics and Operations Research ( email )

Oskar-Morgenstern-Platz 1
Vienna, A-1090
Austria

Center for Financial Studies (CFS) ( email )

Gr├╝neburgplatz 1
Frankfurt am Main, 60323
Germany

Rodrigo Herrera

University of Talca ( email )

2 Norte 685
Talca, 3460000
Chile

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