Approximation of aggregate and extremal losses within the very heavy tails framework |
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| Authors: | Ivan K Mitov Svetlozar T Rachev Frank J Fabozzi |
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| Institution: | 1. Faculty of Mathematics and Informatics , Sofia University , ‘St. Kliment Ohridski’, 1164 Sofia, Bulgaria;2. FinAnalytica Inc. , 1407 Sofia, 21A Srebarna Str., Bulgaria ivan.mitov@finanalytica.com;4. FinAnalytica Inc. , 1407 Sofia, 21A Srebarna Str., Bulgaria;5. Econometrics and Mathematical Finance , School of Economics and Business Engineering, University of Karlsruhe and KIT , Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128 Karlsruhe, Germany;6. Department of Statistics and Applied Probability , University of California , Santa Barbara, CA, USA;7. Yale School of Management , 135 Prospect Street, Box 208200, New Haven, CT 06520-8200, USA |
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| Abstract: | 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. |
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| Keywords: | Operational risk modeling Loss distribution approach Basel II Capital Accord Approximating processes Monte Carlo simulation |
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