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.
Highlights
Operational risk is defined according to Basel II (Nicolas & Firzli, 2011) as well as according to European Solvency II which adopted for insurance industry is defined in the following way (Nicolas & Firzli, 2011)
This paper introduces the state of the art techniques in operational risk modeling
It begins by presenting Solvency II and Basel II criteria
Summary
Operational risk is defined according to Basel II (Nicolas & Firzli, 2011) as well as according to European Solvency II which adopted for insurance industry is defined in the following way (Nicolas & Firzli, 2011). In order to analyse operational risk in insurance, Solvency II Directive (Mittnik, 2011) must be discussed. Quantitative impact study (QIS 5) has encouraged insurance companies to adopt the internal model by structuring the standard approach such that it uses up much more equity (Solvency—European Commission, 2012). In order to analyse the operational risk in this frame, the following assumption will be made: risk will be divided between frequency and severity risk (Doerig, 2000). They will be modeled by Loss Distribution approach (Power, 2005).
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