Peaks over thresholds modelling with multivariate generalized Pareto distributions

TL;DR

This paper develops new methods for multivariate generalized Pareto distributions to model extreme events involving multiple components, with applications in finance and environmental risk assessment.

Contribution

It introduces general construction methods for multivariate GP models, along with inference, threshold selection, diagnostics, and model selection strategies.

Findings

Models fitted to stock returns of UK banks.

Rainfall data modeling for landslide risk.

Proposed methods improve multivariate extreme value analysis.

Abstract

When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions constitutes the multivariate analogue of univariate peaks over thresholds modelling, which is widely used in finance and engineering. We develop general methods for construction of multivariate GP distributions and use them to create a variety of new statistical models. A censored likelihood procedure is proposed to make inference on these models, together with a threshold selection procedure, goodness-of-fit diagnostics, and a computationally tractable strategy for model selection. The models are fitted to returns of stock prices of four UK-based banks and to rainfall data in the context of landslide risk estimation. Supplementary materials and codes are available online.