극단치이론(Extreme Value Theory)과 Value-at-Risk: GPD모형을 중심으로

Most Value at Risk(VaR) models assume normal distribution of financial time series but empirical data show that tails of their distribution are much fatter and unsymmetrical than those of normal distribution. So VaR models based on normal distribution underestimate and miscalculate risk amount and are not adequate for risk management purposes. Extreme Value Theory(EVT) has been recently focused in finance field because it can deal with extreme events extremely well and can estimate tail distribution using only sample data without assuming original distribution. The purpose of this study is to estimate and assess the models for tail-related risk measures by using EVT. In applying EVT to real data, the most important thing is a right selection of threshold point. So the paper introduces two stage subsample bootstrapping method to find an optimal threshold point for GPD model. As expected, GPD model based on more accurate threshold point gives more accurate VaR estimates. It is found that GPD VaR estimates are more accurate than those of GEV, GARCH and RiskMetrics and that EVT models (GPD and GEV) can detect differences in lower tail and upper tail distributions that GARCH and RiskMetrics models cannot. Backtest results also show that GPD model is the best among them in terms of both its accuracy and robustness. Whereas VaR estimates provided by other models, especially GARCH model are very volatile, those of GPD model is stable, which means that GPD model is more useful for practical purposes because minimum required capital amount cannot be changed frequently in reality.