Approximation of aggregate and extremal losses within the very heavy tails framework

Ivan K. Mitov, Svetlozar T. Rachev, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The loss distribution approach is one of the three advanced measurement approaches to the Pillar I modeling proposed by Basel II in 2001. In this paper, one possible approximation of the aggregate and maximum loss distribution in the extremely low frequency/high severity case is given, i.e. the case of infinite mean of the loss sizes and loss inter-arrival times. In this study, independent but not identically distributed losses are considered. The minimum loss amount is considered increasing over time. A Monte Carlo simulation algorithm is presented and several quantiles are estimated. The same approximation is used for modeling the maximum and aggregate worldwide economy losses caused by very rare and very extreme events such as 9/11, the Russian rouble crisis, and the U.S. subprime mortgage crisis. The model parameters are fit on a data sample of operational losses. The respective aggregate and extremal loss quantiles are calculated.

Original languageEnglish
Pages (from-to)1153-1162
Number of pages10
JournalQuantitative Finance
Issue number10
StatePublished - Dec 2010


  • Approximating processes
  • Basel II Capital Accord
  • Loss distribution approach
  • Monte Carlo simulation
  • Operational risk modeling


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