Document Type : Original Research Paper

Authors

• elham alizadeh ¹
• Jafar Haghighat ²
• Hossein asgharpur ³
• Zahra Karimi Takanlu ³

¹ PhD candidate, Faculty of Economics and Management, University of Tabriz, Tabriz, Iran

² Department of Economics, Faculty of Economics and Management, University of Tabriz, Tabriz, Iran

³ Department of Economic Sciences , Faculty of Economics and Management, University of Tabriz, Tabriz, Iran

Abstract

BACKGROUND AND OBJECTIVES: The deviation between risk capital under standard models and its actual amount can pose multiple challenges for insurers. Although the objective of regulatory requirements is to limit insurer risk, these regulations, due to their general nature, are not always applicable to the specific conditions of each company. The standard formula usually operates conservatively and obligates insurers to hold more risk capital than the actual need, which reduces the potential return on equity. Therefore, improving the method of calculating the required capital beyond the standard formula to better describe the effect of risk diversification is essential. In other words, designing alternative approaches and quantifying potential deviations from regulatory standard models should be of concern to insurance managers, legislators, and public policymakers. The aim of this article is to provide a structured model for determining the capital requirements of non-life insurance companies using monthly claims data. To this end, an alternative modeling approach for insurance risk aggregation is proposed, considering two main aspects: the neglect of nonlinear dependencies and company-specific risk parameters. In fact, this model empirically demonstrates the existing gap between the required capital under standard models and capital calculated using alternative approaches. According to this, first, the marginal distribution of each line of business in the insurance portfolio must be parametrically specified to reflect the distributional characteristics of each risk factor. Then, the estimated marginal distributions are aggregated considering the dependency structures between risk factors. It is important to note that the presented modeling approach can be interpreted as a sensitivity analysis of the regulatory framework for capital calculation addressing two often-raised criticisms.
METHODS: To calculate insurance risk, which is the main risk factor in insurance companies, the actual portfolio of the insurance company was considered. To avoid computational complexity, among non-life insurance lines, those with the largest share of premium in the year 1402 were used, namely: third-party liability, Car Body, accident, liability, and fire. The data include monthly paid claims for five lines in the actual portfolio of Iran Insurance Company from 1395:1 to 1402:8. To estimate the marginal copula functions under the individual risk model, various parametric distributions commonly used in actuarial and operational risk fields were fitted. The appropriate distribution for each claims process was determined based on goodness-of-fit tests and the Akaike information criterion. Dependencies between lines were modeled using different copula functions. Three statistical criteria, including the log-likelihood function, Akaike information criterion, and Bayesian Schwarz criterion, were used to select the best-fitting model among the estimated copulas. Then, based on the selected copula function and its corresponding dependency structure, n pairs of data were simulated. The simulated variables were aggregated to establish the total loss distribution under the multivariate copula. Finally, in the alternative model, the economic capital was calculated using the Value-at-Risk risk measure.
FINDINGS: The analysis of the statistical properties of the data used shows that all insurance lines exhibit right skewness and greater kurtosis compared to the normal distribution, indicating the presence of heavy tails in the examined time series. Therefore, the normal distribution is not a suitable distribution for modeling insurance risk. The parameter estimation results of theoretical distributions indicate that the log-normal distribution is the best fit for the historical claim data in four lines: accident, fire, Car Body, and third-party liability, while the generalized Pareto distribution is the best fit for the liability insurance line. It is observed that the most appropriate copula function, based on the highest maximum likelihood value and the lowest information criteria, for interpreting dependency in the insurance portfolio, is the R-Vine copula, which outperforms other copula functions. The size of insurance risk based on real data for the year 1402, according to the risk coefficients in Regulatory Directive No. 69, is approximately 265,235,960 trillion IRR. In the alternative model, which is a combined model of the R-Vine copula with using the Value-at-Risk measure, the results show that the standard model estimates the required insurance risk capital to be on average 25.6% higher than the alternative model at various confidence levels.
CONCLUSION: The overestimation of capital requirements identified in standard models suggests that insurers can significantly reduce their risk capital by taking into account nonlinear dependencies and their own firm-specific risk parameters. Hence, based on empirical observations, it is recommended that regulators incorporate dependency assumptions to reduce discrepancies between the risk capital derived from the standard model and its actual magnitude.

Keywords

• "Capital Requirements"
• "Copula"
• "Economic Capital"
• "Non-life Insurance"
• "R-Vine.Copula"
• "Value at Risk "

Main Subjects

• Economics of finance / insurance