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

Title & Authors
Estimation of VaR Using Extreme Losses, and Back-Testing: Case Study
Seo, Sung-Hyo; Kim, Sung-Gon;

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.
Keywords
Extreme value theory;Value at Risk;KOSPI;back-testing;
Language
Korean
Cited by
1.
Vector at Risk와 대안적인 VaR,홍종선;한수정;이기쁨;

응용통계연구, 2016. vol.29. 4, pp.689-697
1.
Vector at Risk and alternative Value at Risk, Korean Journal of Applied Statistics, 2016, 29, 4, 689
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