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Estimation of VaR Using Extreme Losses, and Back-Testing: Case Study

극단 손실값들을 이용한 VaR의 추정과 사후검정: 사례분석

  • Seo, Sung-Hyo (Division of Chronicle Disease Surveillance, Korea Centers for Disease Control and Prevention) ;
  • Kim, Sung-Gon (Department of Statistics, University of Seoul)
  • 서성효 (질병관리본부 만성병조사과) ;
  • 김성곤 (서울시립대학교 통계학과)
  • Received : 20091000
  • Accepted : 20100300
  • Published : 2010.04.30

Abstract

In index investing according to KOSPI, we estimate Value at Risk(VaR) from the extreme losses of the daily returns which are obtained from KOSPI. To this end, we apply Block Maxima(BM) model which is one of the useful models in the extreme value theory. We also estimate the extremal index to consider the dependency in the occurrence of extreme losses. From the back-testing based on the failure rate method, we can see that the model is adaptable for the VaR estimation. We also compare this model with the GARCH model which is commonly used for the VaR estimation. Back-testing says that there is no meaningful difference between the two models if we assume that the conditional returns follow the t-distribution. However, the estimated VaR based on GARCH model is sensitive to the extreme losses occurred near the epoch of estimation, while that on BM model is not. Thus, estimating the VaR based on GARCH model is preferred for the short-term prediction. However, for the long-term prediction, BM model is better.

References

  1. 박상우, 장인식 (2003). 극단간 이론을 이용한 우리나라 주가지수의 VaR 의 추정, <응용통계>, 18, 59-86.
  2. 이재득 (2003). 한국의 선물가격 변동성과 비대칭성분석: GARCH, EGARCH, TARCH분석, <한국경제통상학회>, 21, 145-170.
  3. 황선영, 박진아 (2005). VaR (Value at Risk) for Korean financial time series, <한국데이터정보과학회지>,16, 283-288.
  4. 황선영, 최문선, 도종두 (2009). 사후검정(Back-testing)을 통한 다변량-GARCH 모형의 평가: 사례분석, <응용통계 연구>, 22, 261-270.
  5. Bekiros, S. D. and Georgoutsos, D. A. (2005). Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance, Journal of International Financial Markets, Institutions & Money, 15, 209-228. https://doi.org/10.1016/j.intfin.2004.05.002
  6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  7. Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer-Verlag, London.
  8. Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues, Quantitative Finance, 1, 223-236. https://doi.org/10.1080/713665670
  9. 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
  10. Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events, Springer.
  11. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
  12. Hull, J. C. (2003). Options, Futures and Other Derivatives, 5th ed., Prentice Hall.
  13. Jorion, P. (2000). Value at Risk, 2nd ed., McGraw Hill, New York.
  14. Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 11, 122-150.

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