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Abstract
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The purpose of this study is to evaluate the forecasting ability of GARCH-type models in
estimating the Value-at-Risk (VaR) by introducing a new four-parameter distribution, called
Exponentiated Odd Log-Logistic Normal distribution. The statistical properties of new heavytailed distribution are investigated and a simulation study is performed to assess the
maximum likelihood estimations of introduced distribution. Then, the VaR is forecasted by
using mean and volatility forecasts and quantile estimation of introduced distribution. Daily
VaR forecasting ability of proposed two-stage model is compared with the GARCH models
specified under heavy-tailed distributions by means of two backtesting methods. Empirical
findings show that proposed two-stage model outperforms to well-known distributions such
as normal, Student’s-t, generalized error, and skewed generalized error distributions at high
quantiles.
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