Operational Risk Modelling in Insurance and Banking

Ognjen Vukovic

Department for Finance, University of Liechtenstein, Vaduz, Liechtenstein.

DOI: 10.4236/jfrm.2015.43010                

Abstract

The author of the presented paper is trying to develop and implement the model that can mimic the state of the art models of operational risk in insurance. It implements generalized Pareto distribution and Monte Carlo simulation and tries to mimic and construct operational risk models in insurance. At the same time, it compares lognormal, Weibull and loglogistic distribution and their application in insurance industry. It is known that operational risk models in insurance are characterized by extreme tails, therefore the following analysis should be conducted: the body of distribution should be analyzed separately from the tail of the distribution. Afterwards the convolution method can be used to put together the annual loss distribution by combining the body and tail of the distribution. Monte Carlo method of convolution is utilized. Loss frequency in operational risk in insurance and overall loss distribution based on copula function, in that manner using student-t copula and Monte Carlo method are analysed. The aforementioned approach represents another aspect of observing operational risk models in insurance. This paper introduces: 1) Tools needed for operational risk models; 2) Application of R code in operational risk modeling;3) Distributions used in operational risk models, specializing in insurance; 4) Construction of operational risk models.

Keywords

Insurance, Operational Risk, Monte Carlo, Statistical Distributions, Modeling, Copula, Convolution, Loss Frequency, Severity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	(2012). Solvency—European Commission. Ec.europa.eu.
[2]	Accords, B. (2006). Basel II: Revised International Capital Framework.
[3]	Bracewell, R. (1986). The Fourier Transform and Its Applications (2nd ed.). New York: McGraw-Hill.
[4]	CEA—Groupe Consultatif (2005). Solvency II Glossary—European Commission.
[5]	Damelin, S., & Miller, W. (2011). The Mathematics of Signal Processing. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9781139003896
[6]	Doerig, H. U. (2000). Operational Risks in Financial Services: An Old Challenge in a New Environment. Switzerland: Credit Suisse Group.
[7]	Embrechts, P., Kluppelberg, C., & Mikosch, T. (1997). Modelling Extremal Events. Berlin: Springer. http://dx.doi.org/10.1007/978-3-642-33483-2
[8]	Hazewinkel, M. (Ed.) (2001). Probability Distribution. Encyclopedia of Mathematics. Berlin: Springer.
[9]	Longin, F. (1997). From Value at Risk to Stress Testing: The Extreme Value Approach. Ceressec Working Paper, Paris: ESSEC.
[10]	Mittnik, S. (2011). Solvency II Calibrations: Where Curiosity Meets Spuriosity. Munich: Center for Quantitative Risk Analysis (CEQURA), Department of Statistics, University of Munich.
[11]	Nelsen, R. B. (1999). An Introduction to Copulas. New York: Springer. http://dx.doi.org/10.1007/978-1-4757-3076-0
[12]	Nicolas, M., & Firzli, J. (2011). A Critique of the Basel Committee on Banking Supervision. Paris: Revue Analyse Financière.
[13]	Power, M. (2005). The Invention of Operational Risk. Review of International Political Economy, 12, 577-599.
[14]	PWC Financial Services Regulatory Practice (2014). Operational Risk Capital: Nowhere to Hide. http://www.pwc.com/us/en/financial-services/regulatory-services/publications/operational-risk-capital.jhtml
[15]	Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges (pp. 229-231). Paris: Publications de l’Institut de Statistique de l’Université de Paris.