The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Estimation of the Expected Loss per Exposure of Export Insurance using GLM

일반화 선형모형을 이용한 수출보험의 지급비율 추정

  • Ju, Hyo Chan (Department of Actuarial Science/Mathematics, Sungkyunkwan University) ;
  • Lee, Hangsuck (Department of Actuarial Science/Mathematics, Sungkyunkwan University)
  • 주효찬 (성균관대학교 보험계리학과/수학과) ;
  • 이항석 (성균관대학교 보험계리학과/수학과)
  • Received : 2013.06.17
  • Accepted : 2013.11.04
  • Published : 2013.12.31
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Abstract

Export credit insurance is a policy tool for export growth. In the era of free trade under the governance of WTO, export credit insurance is still allowed as one of the few instruments to increase exports. This paper, using data on short-term export insurance contracts issued to foreign subsidiaries of Korean companies, calculates the expected loss per exposure by combining the effect of risk factors (credit rate of foreign importers, size of mother company, and payment period) on loss frequency and loss severity in different levels. We, applying generalized linear models (GLM), first fit loss frequency and loss severity to negative binomial and lognormal distribution, respectively, and then estimate the loss frequency rate per contract and the ratio of loss severity to coverage amount. Finally, we calculate the expected loss per exposure for each level of risk factors by combining these two rates. Based on the result of statistical analysis, we present the implication for the current premium rate of export insurance.

한국을 비롯한 많은 국가에서 수출보험은 수출증진을 위한 수단으로 이용되어 왔다. 무역자유화를 위한 세계무역기구의 출범 이후에도 수출보험은 여전히 수출증진을 위한 주요 수단으로 인식된다. 본 논문은 국내 기업의 해외법인이 체결한 단기수출보험의 자료를 이용하여 수출보험과 관련한 위험요소(수입자의 신용등급, 결제기간, 모기업의 크기)의 각 등급에 따른 보험가입금액 대비 보험금 지급비율을 산출한다. 이를 위해 일반화 선형모형을 활용, 모델 선택과정을 거쳐 사고빈도(frequency)와 사고심도(severity)를 각각 음이항분포와 로그노말분포로 적합한다. 그리고 일반화 선형모형의 분석결과를 바탕으로 사고빈도와 사고심도에 미치는 각 위험요소의 등급에 따른 계약건수 대비 평균 사고발생 비율과 보험가입금액 대비 평균 지급비율을 제시한다. 이후 이를 통합함으로써 각 위험요소의 등급별 지급비율의 기댓값을 추정한다. 그리고 이 결과를 이용하여 요율산정에 대한 시사점을 논의한다.

Keywords

References

  1. Amsden, A. (1989). Asia's Next Giant: South Korea and Late Industrialization, Oxford Unversity Press, Oxford.
  2. Branden, M., Vidmar, T. J. and McKean, J. W. (1988). Drug Interaction and Lethality Analysis, CRC Press, Boca Raton.
  3. Chung, C. and Kim, K. (2011). The effects of short-term export insurance and export credit guarantee to the export performance of small medium sized export companies, Journal of International Trade and Insurance, 12, 1-30. (in Korean)
  4. De Jong, P. and Heller, G. (2008). Generalized Linear Models for Insurance Data, Cambridge University Press, Cambridge.
  5. Dobson, A. (2002). An Introduction to Generalized Linear Models, CRC Press, Florida.
  6. Fu, L. and Moncher, R. (2000). Severity distributions for GLMs: Gamma or lognormal? Evidence from Monte Carol simulations, Discussion paper, Available from: www.casact.org/pubs/dpp/dpp04/04dpp149.pdf
  7. Haberman, S. and Renshaw, A. (1996). Generalized linear models and actuarial science, Journal of the Royal Statistical Society, Series D, 45, 407-436.
  8. Holler, K., Sommer, D. and Trahair, G. (1999). Something old, something new in classification ratemaking with a novel use of GLMs for credit insurance, Discussion Paper, Available from: www.casact.org/pubs/forum/99wforum/wf99031.pdf
  9. Johnson, C. (1982). MITI and the Japanese Miracle: The Growth of Industrial Policy, 1925-1975, Stanford University Press, Stanford.
  10. Ki, S. D. and Kim, D. H. (2009). Study on the calculating relative risk for vehicle insurance premium rate using GLM, Research paper, Korean Insurance Research Institute, Seoul. (in Korean)
  11. Kim, H. (2012). A comparative study on the effects of short-term export credit insurance on exports before and after the global financial crisis, Journal of International Trade and Insurance, 13, 29-46. (in Korean)
  12. Korean Trade Insurance Corporation. Glossary of trade and insurance, Available from: www.ksure.or.kr/jsp/info/pop GlsInq.jsp
  13. Lee, I. J. and Lee, E. J. (2000). An empirical study on the effect of export credit insurance on export, Journal of International Trade and Insurance, 1, 235-288. (in Korean)
  14. Mack, T. (1994). Which stochastic model is underlying the chain ladder method? Insurance: Mathematics and Economics, 15, 133-138. https://doi.org/10.1016/0167-6687(94)90789-7
  15. McNeil, A. and Wendin, J. (2007). Bayesian inference for generalized linear mixed models of portfolio credit risk, Journal of Empirical Finance, 14, 131-149. https://doi.org/10.1016/j.jempfin.2006.05.002
  16. Murphy, K., Brockman, M. and Lee, P. (2000). Using generalized linear models to build dynamic pricing systems, Discussion Paper, Available from: www.casualtyactuarialsociety.net/pubs/forum /00wforum/00wf107.pdf
  17. Myers, R., Montgomery, D. and Vining, G. (2002). Generalized Linear Models with Applications in Engineering and the Sciences, John Wiley & Sons, New York.
  18. Nelder, J. and Wedderburn, R. (1972). Generalized linear models, Journal of Royal Statistical Society, 135, 135-370.
  19. Park, C. K. (2002). The problem with, and remedy for, current premium rate of export insurance: the case of short-term export credit insurance, Journal of International Trade and Insurance, 3, 53-64.
  20. Park, C. K. and Shin, D. C. (2000). Study on the appropriate level of export insurance fund and the loss ratio, Journal of International Trade and Insurance, 1, 63-92. (in Korean)
  21. Shin, Y. and Kim, H. (2011). An analysis of the effect of export credit insurance on export using a structural vector error correction model (VECM), Journal of International Trade and Insurance, 12, 23-40. (in Korean)
  22. Wade, R. (1990). Governing the Market: Economic Theory and the Role of Government in East Asian Industrialization, Princeton University Press, Princeton