Journal of the Korean Data & http://dx.doi.org/10.7465/jkdi.2016.27.6.1661 Information Science Society 한국데이터정보과학회지 2016, 27(6), 1661–1671 The GARCH-GPD in market risks modeling: An empirical exposition on KOSPI Cheru Atsmegiorgis 1 · Jongtae Kim 2 · Sanghoo Yoon 3 1 Department of Statistics, Daegu University 23 Department of Computer Science and Statistics Received 31 October 2016, revised 24 November 2016, accepted 24 November 2016 Abstract Risk analysis is a systematic study of uncertainties and risks we encounter in busi- ness, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Ko- rean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models. Keywords: ARMA, GARCH, GARCH-GPD, KOSPI, Value at Risk. 1. Introduction Recent researches, especially in the latter half of 20th century, dealt with the determi- nation of an explicit trade-off between risk and returns. The specific definition of risk is very important when used as the stochastic discount factors for asset pricing, it is equally important to estimate an aggregate measure of risk in portfolio of asset for determination of risk capital. In a financial risk management, the modeling of extreme market risks and its impact are important topics. Extreme market risk is risk due to extreme changes in prices (Ruppert, 2004), e.g. stock market crashes. Although the risk occurs with small probability, it has large financial consequences. The estimation of the daily Value at Risk (VaR) and expected shortfall measures are indispensable to study and understand the risk with respect to the extreme market events. The aim of this paper is to examine and compare the ability of GARCH (Generalized Auto Regressive Conditional Heteroscedasticity) model with normal, t, generalized hyperbolic innovations and GARCH-EVT (Extreme Value Theory) modeling that are used for modeling 1 Ph.D. candidate, Department of statistics, Daegu University, Gyeongsan 38453. 2 Professor, Department of computer science and statistics, Daegu University, Gyeongsan 38453. 3 Corresponding author: Assistant professor, Department of computer science and statistics, Daegu Uni- versity, Gyeongsan 38453, Korea. Email: statstar@daegu.ac.kr