응용통계연구 (The Korean Journal of Applied Statistics)

  • 제23권3호
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  • Pages.471-485
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  • 2010
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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점과정 기법을 이용한 VaR추정의 성과

Performance of VaR Estimation Using Point Process Approach

  • 여성칠 (건국대학교 응용통계학과) ;
  • 문성주 (경상대학교 수산경영학과)
  • Yeo, Sung-Chil (Department of Applied Statistics, Konkuk University) ;
  • Moon, Seoung-Joo (Department of Fisheries Business Administration, GyeongSang National University)
  • 투고 : 20100300
  • 심사 : 20100400
  • 발행 : 2010.06.30
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초록

금융위험의 위험관리를 위한 도구로서 현재 VaR가 널리 이용되고 있다. VaR의 측정은 사용의 편리상 정규분포를 가정하여 이루어져 왔으나 좀 더 정확한 VaR의 산출을 위해 최근 극단치이론을 이용한 추정방법이 관심을 끌고 있다. 지금까지 극단치이론을 이용하여 VaR의 추정을 위한 확률모형에는 주로 GEV모형과 GPD모형이 사용되고 있다. 본 논문에서는 기존의 EV모형이 갖는 문제점들을 극복하고 좀 더 정확한 VaR를 측정하기위한 노력으로 PP모형을 제시하였다. PP모형은 확률과정의 관점에서 GEV모형과 GPD모형을 포괄하는 모형으로서 기존의 EV모형을 일반화시키는 모형이라고 할 수 있다. PP모형이 기존의 정규분포와 두 EV모형에 비해 VaR추정의 성과가 우수함을 실증분석을 통해 보여주었다.

VaR is used extensively as a tool for risk management by financial institutions. For convenience, the normal distribution is usually assumed for the measurement of VaR, but recently the method using extreme value theory is attracted for more accurate VaR estimation. So far, GEV and GPD models are used for probability models of EVT for the VaR estimation. In this paper, the PP model is suggested for improved VaR estimation as compared to the traditonal EV models such as GEV and GPD models. In view of the stochastic process, the PP model is regarded as a generalized model which include GEV and GPD models. In the empirical analysis, the PP model is shown to be superior to GEV and GPD models for the performance of VaR estimation.

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과제정보

연구 과제 주관 기관 : 건국대학교

참고문헌

  1. Balkema, A. A. and de Haan, L. (1974). Residual lifetime at great age, Annals of Probability, 2, 792-804. https://doi.org/10.1214/aop/1176996548
  2. Berkowitz, J. and O'Brien, J. (2002). How accurate are Value-at-Risk models at commercial banks?, Journal of Finance, 57, 1093-1112. https://doi.org/10.1111/1540-6261.00455
  3. Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer, London.
  4. Cox, D. R. and Isham, V. (1980). Point Processes, Chapman and Hall, London.
  5. Danielsson, J. and de Vries, C. G. (1997a). Tail index and quantile estimation with very high frequency data, Journal of Empirical Finance, 4, 241-257. https://doi.org/10.1016/S0927-5398(97)00008-X
  6. Danielsson, J. and de Vries, C. G. (1997b). Value at Risk and extreme returns, In Extremes and Integrated Risk Management(ed. Embrechts, P.), 85-106, Risk Waters Group, London.
  7. Duffie, D. and Pan, J. (1997). An overview of Value at Risk, Journal of Derivatives, 4, 7-49. https://doi.org/10.3905/jod.1997.407971
  8. Embrechts, P., Klupppelberg, C. and Mikosh, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer, Berlin.
  9. Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 180-190. https://doi.org/10.1017/S0305004100015681
  10. Hill, B. M. (1975).A simple general approach to inference about the tail of a distribution, Annals of Statistics, 33, 1163-1174.
  11. Jarque, C. M. and Bera, A. K. (1987). A test for normality of observations and regression residuals, International Statistical Review, 55, 163-172. https://doi.org/10.2307/1403192
  12. Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological events, Quarterly Journal of the Royal Meteorological Society, 81, 158-172. https://doi.org/10.1002/qj.49708134804
  13. Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed., McGraw-Hill, New York.
  14. Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 2, 73-84. https://doi.org/10.3905/jod.1995.407918
  15. Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin.
  16. McNeil, A. J. (1997). Estimating the tails of loss severity distributions using extreme value theory, ASTIN Bulletin, 27, 117-137. https://doi.org/10.2143/AST.27.1.563210
  17. McNeil, A. J. and Frey, R. (2000). Estimation of tail-related risk for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance, 7, 271-300. https://doi.org/10.1016/S0927-5398(00)00012-8
  18. McNeil, A. J. and Saladin, T. (1997). The Peaks over Thresholds Methods for Estimating High Quantiles of Loss Distributions, Proceedings of 28th International ASTIN Colloquium.
  19. Neftci, S. (2000). Value at Risk calculations, extreme events, and tail estimation, The Journal of Derivatives, 23-37.
  20. Pickands, J. (1971). The two-dimensional poisson process and extremal processes, Journal of Applied Probability, 8, 745-756. https://doi.org/10.2307/3212238
  21. Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131. https://doi.org/10.1214/aos/1176343003
  22. Reiss, R. D. and Thomas, M. (2001). Statistical Analysis of Extreme Values, 2nd ed., Birkhauser Verlag, Basel.
  23. Resnick, S. I. (1986). Point process, regular variation and weak convergence, Advances in Applied Probability, 18, 66-138. https://doi.org/10.2307/1427239
  24. Smith, R. L. (1989). Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone(with discussion), Statistical Science, 4, 367-393. https://doi.org/10.1214/ss/1177012400
  25. Smith, R. L. and Shively, T. S. (1995). Point process approach to modeling trends in tropospheric ozone based on exceedances of a high threshold, Atmospheric Environment, 29, 3489-3499. https://doi.org/10.1016/1352-2310(95)00030-3
  26. von Mises, R. (1936). La distribution de la plus grande de n valeurs, Revere Mathematical Union Interbalcanique, 1, 141-160.
  27. Yeo, S. C. (2006). Performance analysis of VaR and ES based on extreme value theory, The Korean Communications in Statistics, 13, 389-407. https://doi.org/10.5351/CKSS.2006.13.2.389