An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates

An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates

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Article ID: iaor20162997
Volume: 83
Issue: 3
Start Page Number: 735
End Page Number: 776
Publication Date: Sep 2016
Journal: Journal of Risk and Insurance
Authors: , ,
Keywords: insurance, maximum likelihood estimation, value at risk, Poisson process, correlation, confidence interval
Abstract:

A general methodology for modeling loss data depending on covariates is developed. The parameters of the frequency and severity distributions of the losses may depend on covariates. The loss frequency over time is modeled with a nonhomogeneous Poisson process with rate function depending on the covariates. This corresponds to a generalized additive model, which can be estimated with spline smoothing via penalized maximum likelihood estimation. The loss severity over time is modeled with a nonstationary generalized Pareto distribution (alternatively, a generalized extreme value distribution) depending on the covariates. Since spline smoothing cannot directly be applied in this case, an efficient algorithm based on orthogonal parameters is suggested. The methodology is applied both to simulated loss data and a database of operational risk losses collected from public media. Estimates, including confidence intervals, for risk measures such as Value‐at‐Risk as required by the Basel II/III framework are computed. Furthermore, an implementation of the statistical methodology in R is provided.

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