Statistical Modeling of Insurance Data via Vine Copula (original) (raw)
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Modeling Bivariate Dependency in Insurance Data via Copula: A Brief Study
Journal of Risk and Financial Management
Copulas are a quite flexible and useful tool for modeling the dependence structure between two or more variables or components of bivariate and multivariate vectors, in particular, to predict losses in insurance and finance. In this article, we use the VineCopula package in R to study the dependence structure of some well-known real-life insurance data and identify the best bivariate copula in each case. Associated structural properties of these bivariate copulas are also discussed with a major focus on their tail dependence structure. This study shows that certain types of Archimedean copula with the heavy tail dependence property are a reasonable framework to start in terms modeling insurance claim data both in the bivariate as well as in the case of multivariate domains as appropriate.
A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas
Asian Development Policy Review, 2017
This paper deals with the risks aggregation issue and adequate risk capital modeling within a multivariate setting. Focusing on the non-life insurance risk module, we examine the sensitivity of capital requirement to the dependence among risks for a multi-line Tunisian insurance firm. Such a context entails a nonlinear dependence of risks problem whose resolution may be intended by means of multivariate copulas. The relevant analysis relies profoundly on the dependence modeling by the means of vine copulas which are a flexible technique to model multivariate distributions constructed using a cascade of bivariate copulas. Under various confidence levels in VaR and TailVaR, the reached findings reveal the advantages of D-Vine copula in modeling inhomogeneous structures of dependency due to its flexibility of use in a simulation context. Practitioners and regulators can explore our conclusions for the assessment of risk capital under Solvency 2, which is based on stochastic models. Contribution/ Originality: This study uses new methodology based on CD-vine copulas estimation to investigate the sensitivity of solvency capital requirement to the dependence pattern between the losses derived from non-life business lines of a Tunisian insurance company.
Financial dependence analysis: applications of vine copulas
Statistica Neerlandica, 2013
This paper features the application of a novel and recently developed method of statistical and mathematical analysis to the assessment of nancial risk: namely Regular Vine copulas. Dependence modelling using copulas is a popular tool in nancial applications, but is usually applied to pairs of securities. Vine copulas oer greater exibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which can be arranged and analysed in a tree structure to facilitate the analysis of multiple dependencies. We apply Regular Vine copula analysis to a sample of stocks comprising the Dow Jones Index to assess their interdependencies and to assess how their correlations change in dierent economic circumstances using three dierent sample periods: pre
A two-component copula with links to insurance
Dependence Modeling
This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit of copulas for the insurance industry.
Risk Measurement and Risk Modelling Using Applications of Vine Copulas
Sustainability, 2017
This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. The paper features the use of Regular Vine copulas in an analysis of the co-dependencies of 10 major European Stock Markets, as represented by individual market indices and the composite STOXX 50 index. The sample runs from 2005 to the end of 2013 to permit an exploration of how correlations change indifferent economic circumstances using three different sample periods: pre
Financial Dependence Analysis: Applications of Vine Copulae
2013
This paper features the application of a novel and recently developed method of statistical and mathematical analysis to the assessment of nancial risk: namely Regular Vine copulas. Dependence modelling using copulas is a popular tool in nancial applications, but is usually applied to pairs of securities. Vine copulas oer greater exibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which can be arranged and analysed in a tree structure to facilitate the analysis of multiple dependencies. We apply Regular Vine copula analysis to a sample of stocks comprising the Dow Jones Index to assess their interdependencies and to assess how their correlations change in dierent economic circumstances using three dierent sample periods: pre
Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals
Studies in Nonlinear Dynamics & Econometrics, 2019
This paper investigates dependence among insurance claims arising from different lines of business (LoBs). Using bivariate and multivariate portfolios of losses from different LoBs, we analyse the ability of various copulas in conjunction with skewed generalised hyperbolic (GH) marginals to capture the dependence structure between individual insurance risks forming an aggregate risk of the loss portfolio. The general form skewed GH distribution is shown to provide the best fit to univariate loss data. When modelling dependency between LoBs using one-parameter and mixture copula models, we favour models that are capable of generating upper tail dependence, that is, when several LoBs have a strong tendency to exhibit extreme losses simultaneously. We compare the selected models in their ability to quantify risks of multivariate portfolios. By performing an extensive investigation of the in- and out-of-sample Value-at-Risk (VaR) forecasts by analysing VaR exceptions (i.e. observations ...
Copula Approach for Modelling Dependence Structure
Nwsa Physical Sciences, 2012
This paper introduces the concept of copula as a tool to describe relationships among multivariate random variables. In this study, under the assumption of data can be modelled by one of Archimedean copulas (Gumbel, Frank, Clayton), the dependence structure between two dependent random variables with Weibull marginals is modelled by using copula.
2009
Recibido para revisar junio 11 de 2008, aceptado noviembre 2 de 2008, versión final noviembre 13 de 2008 RESUMEN: El modelamiento en problemas que involucran datos bivariados dependientes es muy importante en diversas áreas del conocimiento, tales como: finanzas, actuaría, confiabilidad y análisis de supervivencia. En la literatura, se conocen algunos modelos cópula que han sido ampliamente utilizados para modelar distribuciones multivariadas dependientes, entre los cuales se destaca la clase de cópulas Arquimedianas. En este artículo, se presenta una metodología para seleccionar entre algunos modelos cópula Arquimedianos el que mejor se ajusta a un conjunto de datos dependientes, utilizando gráficos de bondad de ajuste, gráficos cuantil cuantil (Q-Q plot) y la prueba analítica de bondad de ajuste de Cramér-von Mises. Se realizó una aplicación de la metodología con datos simulados y utilizando datos de siniestros en pólizas de seguro. Los resultados mostraron que los datos de seguros se ajustan a un modelo bivariado basado en la cópula Frank con marginales lognormales.
The Simulation of Dependent Insurance Company's Losses Employing Copulas
isd.ktu.lt
The research is performed in the field of risk management of insurance company's activity. The simulation model that allows to evaluate the dependency between two types of insurance company's losses is presented in this paper. Since the company's losses are dependent only in the right tails of distributions and are not normally distributed, the application of Pearson's correlation coefficient would be inadequate. For their dependency structure, the alternative method -copula -is employed, which allows to construct the non-linear dependency structure between the dependent stochastic variables despite their type of distributions. The purpose of this work is to explore the copula effect on the liability portfolio of the insurance company. The developed simulation model is based on Piece Linear Aggregates (PLA) approach.