Journal
ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION
Volume 37, Issue 2, Pages 265-291Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.2143/AST.37.2.2024067
Keywords
extreme value theory; g-and-h distribution; hill estimator; LDA; operational risk; peaks over threshold; second order regular variation; subadditivity; value-at-risk
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Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate. In our paper, we discuss some fundamental properties of the g-and-h distribution and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto distribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-and-h distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, superadditivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.
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