Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Analyzing rainfall patterns and pricing rainfall insurance using copula

코퓰라를 이용한 강수의 패턴 분석과 강수 보험의 가격 결정

  • Received : 2013.02.04
  • Accepted : 2013.05.21
  • Published : 2013.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper proposes analyzing monthly rainfall patterns using copula and pricing related rainfall insurance using it. We analyze 30-year monthly precipitation data for 9 Korean cities between June and September using copula showing so that it can effectively generate realistic monthly rainfall patterns. In addition, we show that our copula rainfall models can be used in pricing various kinds of rainfall insurances effectively.

최근 들어 예측하기 힘든 기후의 변동성이 심해지고 한국의 산업이 고도화됨에 따라 날씨의 변화에 능동적으로 대처하기 위해 날씨보험이나 날씨 파생상품을 활용할 수 있으나 현재 실제로 이러한 금융상품을 이용하여 날씨위험을 관리하는 데에는 많은 어려움과 한계가 있다. 본 논문에서는 다양한 강수보험의 활성화에 필요한 강수횟수와 강수량의 확률적 모델링을 통하여 여러 가지 강수 보험을 제안하고 추정된 결합분포를 통하여 보험료를 산출하려 한다. 이를 위하여 최근 30년 동안 한국 9개 지역의 7월-9월의 월 강수량과 월 강수 횟수를 확률분포에 적합하고 두 확률변수의 상관성을 코퓰라를 이용하여 분석한다. 그리고 개별분포와 추정된 코퓰라를 이용하여 시뮬레이션을 통하여 여러 가지 강수 보험의 가격을 결정하는 방법을 제안한다.

Keywords

References

  1. Alaton, P., Djehiche, B. and Stillberger, D. (2002). On modelling and pricing weather derivatives. Applied Mathematical Finance, 9, 1-20. https://doi.org/10.1080/13504860210132897
  2. Benth, F. E. and Saltyte-Benth, J. (2007). The volatility of temperature and pricing of weather derivatives. Quantitative Finance, 7, 553-561. https://doi.org/10.1080/14697680601155334
  3. Berg, D. and Bakken, H. (2006). Copula goodness-of-fit tests: A comparative study, Department of Mathematics, University of Oslo, Oslo, Norway.
  4. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-655. https://doi.org/10.1086/260062
  5. Bouye, E., Durrleman, V., Nikeghbali, A., Riboulet, G. and Roncalli, T. (2000). Copulas for finance: A reading guide and some applications, Groupe de recherche operationnelle credit Lyonnais, Paris.
  6. Brockett, P. L., Golden, L. L., Wen, M. and Yang, C. C. (2009). Pricing weather derivatives using the indifference pricing approach. North American Actuarial Journal, 13, 303-315. https://doi.org/10.1080/10920277.2009.10597556
  7. Cao, M. and Wei, J. (2000). Pricing the weather. Risk, 13, 67-70.
  8. Cao, M., Li, A. and Wei, J. (2004). Precipitation modeling and contract valuation: A frontier in weather derivatives. The Journal of Alternative Investments, 7, 93-99. https://doi.org/10.3905/jai.2004.439656
  9. Carmona, R. and Diko, P. (2005). Pricing precipitation based derivatives. International Journal of Theoretical and Applied Finance, 8, 959-988. https://doi.org/10.1142/S0219024905003311
  10. Cherubini, U., Luciano, E. and Vecchiato, W. (2004). Copula methods in finance, John Wiley & Sons, Chichester.
  11. Choi, C., Shin, D. and Kim, C. (2012). Managing weather-risks in Korean city-gas industry using weather derivatives. Korean Journal of Futures and Options, 20, 451-481.
  12. Demarta, S. and McNeil, A. J. (2005). The t copula and related copulas. International Statistical Review, 73, 111-129.
  13. Durrleman, V., Nikeghbali, A. and Roncalli, T. (2000). Which copula is the right one? Groupe de recherche operationnelle credit Lyonnais, Paris.
  14. Embrechts, P., Lindskog, F. and McNeil, A. (2003). Modelling dependence with copulas and applications to risk management. In Handbook of Heavy Tailed Distributions in Finance, Volume 1, edited by S. Rachev, Elsevier, Amsterdam, 331-385.
  15. Fowler, H. J., Kilsby, C. G. and O'Connel, P. E. (2000). A stochastic rainfall model for the assessment of regional water resource systems under changed climatic conditions. Hydrology and Earth System Sciences, 4, 263-282. https://doi.org/10.5194/hess-4-263-2000
  16. Frees, E. and Valdez, E. (1998). Understanding relationships using copulas. North American Actuarial Review, 2, 1-25.
  17. Genest, C., Quessy, J.-F. and ReMillard, B. (2006). Goodness-of-fit procedures for copula models based on the probability integral transformation. Scandinavian Journal of Statistics, 33, 337-366. https://doi.org/10.1111/j.1467-9469.2006.00470.x
  18. Geweke, J. (1991). Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints and the evaluation of constraint probabilities, Computing science and statistics: The twenty-third symposium on the interface, Seattle.
  19. Kim, E. and Lee, T. (2011). A numerical study on portfolio VaR forecasting based on conditional copula, Journal of the Korean Data & Information Science Society, 22, 1065-1074.
  20. Klugman, S., Panjer, H. and Willmot, G. (2008). Loss models: From data to decisions, John Wiley & Sons, New Jersey.
  21. Lee, C., Kwon, H. and Ha, H. (2008). A study on weather insurance pricing based on stochastic temperature modeling. Journal of Insurance Studies, 19, 55-76.
  22. Lee, I. and Kim, S. (2004). Properties of extended gamma distribution, Journal of the Korean Data & Information Science Society, 15, 753-758.
  23. Lee, J. (2002). A study on the valuation of the CDD/HDD weather options. Korean Journal of Financial Studies, 31, 229-255.
  24. Leobacher, G. and Ngare, P. (2011). On modeling and pricing rainfall derivatives with seasonality. Applied Mathematical Finance, 18, 71-91. https://doi.org/10.1080/13504861003795167
  25. Malevergne, Y. and Sornette, D. (2006). Extreme financial risks: From dependence to risk management, Springer, Heidelberg.
  26. Martin, S. W., Barnett, B. J. and Coble, K. H. (2001). Developing and pricing precipitation insurance. Journal of Agricultural and Resource Economics, 26, 261-274.
  27. Moller, T. (2003). Indifference pricing of insurance contracts in a product space model. Finance and Stochastics, 7, 197-217. https://doi.org/10.1007/s007800200086
  28. Moore, K. S. and Young, V. R. (2003). Pricing equity-linked pure endowments via the principle of equivalent utility. Insurance: Mathematics and Economics, 33, 497-516. https://doi.org/10.1016/S0167-6687(03)00166-5
  29. Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
  30. Sanso, B. and Guenni, L. (1999). A stochastic model for tropical rainfall at a single location. Journal of Hydrology, 214, 64-73. https://doi.org/10.1016/S0022-1694(98)00241-8
  31. Schmidt, T. (2007). Coping with copulas. In Copulas: From Theory to Applications in Finance, edited by J. Rank, Risk Books, Torquay, 3-34.
  32. Scholzel, C. and Friederichs, P. (2008). Multivariate non-normally distributed random variables in climate research: Introduction to the copula approach. Nonlinear Processes in Geophysics, 15, 761-772. https://doi.org/10.5194/npg-15-761-2008
  33. Sklar, A. (1959). Functions de reparation rma n dimensions et leurs marges. Publications de l'institut de statistique de l'univiversite de Paris, 8, 229-231.
  34. Stowasser, M. (2012). Modelling rain risk: A multi-order Markov chain model approach. Journal of Risk Finance, 13, 45-60. https://doi.org/10.1108/15265941211191930
  35. Trivedi, P. and Zimmer, D. (2005). Copula modeling: An introduction for practitioners. Foundations and Trends in Econometrics, 1, 61-64.
  36. Wilks, D. S. (1998). Multi site generalization of a daily stochastic precipitation generation model. Journal of Hydrology, 210, 178-191. https://doi.org/10.1016/S0022-1694(98)00186-3
  37. Young, V. R. (2003). Equity-indexed life insurance: pricing and reserving using the principle of equivalent utility. North American Actuarial Journal, 7, 68-86. https://doi.org/10.1080/10920277.2003.10596078

Cited by

  1. Profit analysis of life insurance products with interest rate options vol.24, pp.4, 2013, https://doi.org/10.7465/jkdi.2013.24.4.737
  2. Stochastic simulation of daily precipitation: A copula approach vol.25, pp.1, 2014, https://doi.org/10.7465/jkdi.2014.25.1.245
  3. 코플라함수를 이용한 극단치 강풍과 강수 분석 vol.28, pp.4, 2013, https://doi.org/10.7465/jkdi.2017.28.4.797