학술논문
Risk capital aggregation under the standard framework of Solvency II / Solvency II 표준 제도하에서의 위험 자본 평가
Document Type
Dissertation/ Thesis
Author
Source
Subject
Language
English
Abstract
본 연구는 Cornish Fisher (CF) 근사를 활용하여 총 요구자본 산출 공식을 개선한다. 현행 Risk-Based-Capital(RBC) 제도의 총 요구자본 산출 공식은 각 리스크들이 다변량 정규분포를 따른다는 가정하에 도출되었다. 현실적으로 손실 리스크는 보통 양의 왜도를 지니기 때문에 이러한 정규가정은 실제 리스크를 과소평가할 수 있는 문제점이 존재한다. Sandstrom에 따르면, CF근사를 통해서 이러한 왜도 문제를 해결할 수 있다. 본 연구에서는 CF근사 활용에 있어서 2가지 접근방식을 취한다. 하나는 Sandstrom의 접근 방식인데 전체 회사 포트폴리오의 왜도 추정이 정확하지 못하다는 문제가 있다. 따라서 왜도 추정 방식을 개선한 Sandstrom의 접근 방식을 취한다.다른 하나는 각 리스크에 CF근사를 활용함으로써 Quadratic form으로 변환 후 이에 대한 분포를 이용하여 총 요구자본을 산출한다.시뮬레이션을 통해 현행 표준공식, Sandstrom 공식들, quadratic form을 활용한 새로운 공식을 비교한다. 여기서, Sandstrom 공식에는 왜도 추정 방식에 따라 Sandstrom 방식, CF근사를 한번 더 한 후 MME로 추정하는 방식, Quadratic form의 분포로부터 추정하는 방식으로 총 3가지가 존재한다. 시뮬레이션 결과 Sandstrom의 공식에 총 리스크의 왜도를 Quadratic form의 분포로 추정하는 방식을 사용한 공식이 MSE의 측면에서 가장 좋은 것으로 나타난다.
This study uses CF expansion to improve the total required capital formula for Risk-Based-Capital(RBC) ratio. The current RBC system’s total required capital formula is derived under the assumption that each loss random variable follows a multivariate normal distribution. But, the actual loss distribution usually shows positive skewness. So, there is a problem that can be underestimated than actual loss. According to Sandstr¨om (2007) CF expansion can solve the skewness problem. In this study, two approaches are taken in the application of CF expansion. One is Sandstrom’s approach and also the problem of Sandstrom’s approach is that the skewness estimate of the entire company’s portfolio is not accurate. Thus, the Sandstrom approach is taken, which has improved the method of estimating skewness. The other uses CF expansion for each risk to convert to Quadratic form and then use the distribution to calculate the total required capital. Through simulation, the current standard formula, Sandstrom formulas, and the formula by new approach. Here, there are 3 version of Sandstrom formulas: the sandstrom method, moment matching method, and the estimation from the distribution of the Quadratic form to estimate skewness of total loss random variable. The simulationresults show that the Sandstrom formula using skewness estimated from the Quadratic form is the best in terms of MSE.
This study uses CF expansion to improve the total required capital formula for Risk-Based-Capital(RBC) ratio. The current RBC system’s total required capital formula is derived under the assumption that each loss random variable follows a multivariate normal distribution. But, the actual loss distribution usually shows positive skewness. So, there is a problem that can be underestimated than actual loss. According to Sandstr¨om (2007) CF expansion can solve the skewness problem. In this study, two approaches are taken in the application of CF expansion. One is Sandstrom’s approach and also the problem of Sandstrom’s approach is that the skewness estimate of the entire company’s portfolio is not accurate. Thus, the Sandstrom approach is taken, which has improved the method of estimating skewness. The other uses CF expansion for each risk to convert to Quadratic form and then use the distribution to calculate the total required capital. Through simulation, the current standard formula, Sandstrom formulas, and the formula by new approach. Here, there are 3 version of Sandstrom formulas: the sandstrom method, moment matching method, and the estimation from the distribution of the Quadratic form to estimate skewness of total loss random variable. The simulationresults show that the Sandstrom formula using skewness estimated from the Quadratic form is the best in terms of MSE.