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


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.


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