응용통계연구 (The Korean Journal of Applied Statistics)

  • 제28권4호
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  • Pages.703-719
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  • 2015
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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코호트 사망률을 이용한 장수채권 가격산출

Longevity Bond Pricing by a Cohort-based Stochastic Mortality

  • Jho, Jae Hoon (School of International Economics and Business, Yeungnam University) ;
  • Lee, Kangsoo (Korea Insurance Development Institute)
  • 투고 : 2015.07.13
  • 심사 : 2015.07.30
  • 발행 : 2015.08.31
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초록

본 논문은 평균회귀 2요인 사망률 모형에 코호트 효과를 반영한 개선된 확률론적 사망률 모형을 제시한다. 한국 남자의 사망률 자료를 바탕으로 가중평균최소제곱법과 메트로폴리스 알고리듬을 이용하여 사망률 모형을 추정한 결과 코호트 효과를 반영하는 것이 모형 적합도를 향상시킴을 발견하였다. 국민연금공단과 같은 연금사업자가 자신의 장수위험을 금융시장에 순차적으로 전가하는 수단으로서 옵션방식 이자지급 장수채권의 활용을 제안하고 발행채권의 가격 산출방법을 제시하는 것이 본 논문이 기여하는 점이다. 특히 생존지수에 의해 이자지급 현금흐름이 결정되는 장수채권 가격산출을 위하여 코호트 효과가 매우 중요한 요소임을 강조하였다.

We propose an extension of the Lee and Jho (2015) mean reverting the two factor mortality model by incorporating a period-specific cohort effect. We found that the consideration of cohort effect improves the mortality fit of Korea male data above age 65. Parameters are estimated by the weighted least squares method and Metropolis algorithm. We also emphasize that the cohort effect is necessary to choose the base survival index to calculate longevity bond issue price. A key contribution of the article is the proposal and development of a method to calculate the longevity bond price to hedge the longevity risk exposed to Korea National Pension Services.

키워드

참고문헌

  1. Artzner, P., Delbaen, F., Eber, J. M. and Heath, D. (1999). Coherent measures of risk, Mathematical Finance, 9, 203-228. https://doi.org/10.1111/1467-9965.00068
  2. Blake, D. and Burrows, W. (2001). Survivor bonds: Helping to hedge mortality risk, Journal of Risk and Insurance, 68, 339-348. https://doi.org/10.2307/2678106
  3. Blake, D., Boardman, T. and Cairns, A. (2014). Sharing longevity risk: Why governments should issue longevity bonds, North American Actuarial Journal, 18, 258-277. https://doi.org/10.1080/10920277.2014.883229
  4. Borger, M., Fleischer, D. and Kuksin, N. (2014). Modeling the mortality trend under modern solvency regimes, Astin Bulletin, 44(01), 1-38. https://doi.org/10.1017/asb.2013.24
  5. Booth, H., Maindonald, J. and Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336. https://doi.org/10.1080/00324720215935
  6. Cairns, A. J., Blake, D. and Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 687-718. https://doi.org/10.1111/j.1539-6975.2006.00195.x
  7. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A. and Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 13, 1-35. https://doi.org/10.1080/10920277.2009.10597538
  8. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D. and Khalaf-Allah, M. (2011). Mortality density forecasts: An analysis of six stochastic mortality models, Insurance: Mathematics and Economics, 48, 355-367. https://doi.org/10.1016/j.insmatheco.2010.12.005
  9. Continuous Mortality Investigation, Mortality Committee (2009a). A Prototype Mortality Projections Model: Part One-An Outline of the Proposed Approach, CMI Working Paper 38.
  10. Continuous Mortality Investigation, Mortality Committee (2009b). A Prototype Mortality Projections Model: Part Two-Detailed Analysis. CMI Working Paper 39.
  11. Cox, S. H., Lin, Y. and Pedersen, H. (2010). Mortality risk modeling: Applications to insurance securitization, Insurance: Mathematics and Economics, 46, 242-253. https://doi.org/10.1016/j.insmatheco.2009.09.012
  12. Cummins, J. D. (2008). CAT bonds and other risk-linked securities: State of the market and recent developments, Risk Management and Insurance Review, 11, 23-47. https://doi.org/10.1111/j.1540-6296.2008.00127.x
  13. Currie, I. D. (2006). Smoothing and forecasting mortality rates with P-splines, Talk given at the Institute of Actuaries, June 2006, Available from http://www.macs.hw.ac.uk/iain/research/talks/London.2007.pdf.
  14. De Jong, P. and Tickle, L. (2006). Extending Lee-Carter mortality forecasting, Mathematical Population Studies, 13, 1-18. https://doi.org/10.1080/08898480500452109
  15. Hunt, A. and Blake, D. (2015). Modelling longevity bonds: Analysing the Swiss Re Kortis Bond, Insurance: Mathematics and Economics, http://dx.doi.org/10.1016/j.insmatheco.2015.03.017.
  16. Lee, K. and Jho, J. H. (2015). A two factor model with mean reverting process for stochastic mortality, The Korean Journal of Applied Statistics, 28, 393-406. https://doi.org/10.5351/KJAS.2015.28.3.393
  17. Lee, R. D. and Carter, L. R. (1992). Modeling and forecasting US mortality, Journal of the American Statistical Association, 87, 659-671.
  18. Lee, R. and Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 537-549. https://doi.org/10.1353/dem.2001.0036
  19. Ministry of Health & Welfare (2013). The third financial prospect of national pension, Technical report, Available from: http://www.mw.go.kr/front_new/al/sal0301ls.jsp?PAR_MENU_ID=04&MENU_ID=0403
  20. Ministry of Stratage and Finance (2014). Goverment to Promote Private Plans, Press release at 27th of August, Available from: http://www.mosf.go.kr/news/news02.jsp
  21. National Pension Service (2013). Number of Old-age Pensioners by Age Group, Sex & Administrative District, National Pension Statisitcal Yearbook, 212-216.
  22. O'Hare, C. and Li, Y. (2012). Explaining young mortality, Insurance: Mathematics and Economics, 50, 12-25. https://doi.org/10.1016/j.insmatheco.2011.09.005
  23. Plat, R. (2009). On stochastic mortality modeling, Insurance: Mathematics and Economics, 45, 393-404. https://doi.org/10.1016/j.insmatheco.2009.08.006
  24. Renshaw, A. E. and Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570. https://doi.org/10.1016/j.insmatheco.2005.12.001
  25. Salou, J.-M. and Hu, Y.-W. (2006). Overview of the financial wealth accumulated under funded pension arrangements, Pension Markets in Focus, 3, 2-13.
  26. Wang, S. S., Young, V. R. and Panjer, H. H. (1997). Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics, 21, 173-183. https://doi.org/10.1016/S0167-6687(97)00031-0
  27. Wilmoth, J. R. (1993). Computational methods for fitting and extrapolating the Lee-Carter model of mortality change, Technical Report, Department of Demography, University of California, Berkeley.