• The Korean Journal of Financial Management
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• v.23 no.2
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• pp.189-208
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• 2006

In this paper we are concerned with estimation of tail related risk measures for heteroscedastic financial time series and VaR limits that VaR tells us nothing about the potential size of the loss given. So we use GARCH-EVT model describing the tail of the conditional distribution for heteroscedastic financial series and adopt Expected Shortfall to overcome VaR limits. The main results can be summarized as follows. First, the distribution of stock return series is not normal but fat tail and heteroscedastic. When we calculate VaR under normal distribution we can ignore the heavy tails of the innovations or the stochastic nature of the volatility. Second, GARCH-EVT model is vindicated by the very satisfying overall performance in various backtesting experiments. Third, we founded the expected shortfall as an alternative risk measures.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.