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

- Journal title : Korean Journal of Applied Statistics
- Volume 23, Issue 2, 2010, pp.219-234
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2010.23.2.219

Title & Authors

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

Seo, Sung-Hyo; Kim, Sung-Gon;

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

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