Vine Copula 모형에 기반한 손해보험사의 손해액 통합리스크 측정

초록

In measuring the aggregated risk of an insurer's losses, we should consider the risks from individual lines of business and the dependence structure among them. The well-known methodologies to measure the aggregated risk of losses include i) the factor method multiplying the losses by their risk factors and combining them with correlation coefficients, and ii) the shock method measuring changes in expected losses due to shocks to risk drivers. However, this study analyzes the aggregated risk by modeling dependence among insurance risks via a vine copula function. We collected monthly loss data - categorized into four business lines - from non-life insurers in Korea, then estimated a simple sum of univariate value-at-risk (uVaR) called SuVaR and an aggregated copula-based multivariate value-at-risk (mVaR) called AmVaR. The result shows that mVaR estimates are greater than uVaR estimates, which assume independence among business lines. It implies that the copula model is more suitable than the univariate model for measuring integrated risk since it reflects the dependence structure more flexibly. Also, the AmVar estimate is the largest, the variance-covariance VaR is the smallest, and the SuVaR lies between them. The differences in aggregate losses over different methodologies increase, as the confidence level changes from low to high.

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