변동성 모형의 질적 특성에 관한 연구

Abstract

This study analyzed the qualitative characteristics of the volatility model based on various analytical standards. In the analysis of prediction errors according to the empirical analysis results, the prediction errors of EVARCH model compared with RMSE standard were found to be least for 5 and 10 days, and those of GARCH model for 20 and 30 days. But comparing with MAE standard, the prediction model of GARCH model was the least in EGARCH model for 5 days, in EWMA for the 10 days, in GARCH model on 20 and 30 days. In cases of comparison with MAPE standard, EWMA showed the most superior prediction performance. In the analysis of information effectiveness, the implied volatility was found to be most superior during the 20 day prediction period and EGARCH model was superior in the forecast period of 5, 10, and 30 day prediction period. In the unbiased analysis, EMWA model was found to have bias in the freedom in the prediction periods of 10, 20 and 30 days. According to the analysis results of volatility model using the methodology of Davidson and Mackinnon which enables the intuitive comparison of the model, EGARCH model had superior prediction in 5 and 10 day prediction periods and GARCH model has superior prediction performance for 20 and 30 days. Compared with RMSE standard, EGARCH model showed the least prediction errors across all prediction days before the global financial crisis. But the prediction errors were least during 20 days in GARCH and for 30 days in the implied volatility. When comparing with MAE standard, while EGARCH and EWMA showed outstanding prediction performances during the period before the financial crisis, the prediction errors were analysed to be least in GARCH model and EGARCH model. When comparing with MAPE standard, while EWMA showed outstanding prediction performances during all prediction days before the financial crisis, the prediction errors were found to be least in GARCH model and EGARCH model in the period after the financial crisis. The implied volatility of the information effectiveness was shown to be highest during the period after the financial crisis but the information effectiveness of EGARCH model was higher. EWMA model, regardless of the period of the financial crisis, showed characteristics of unbiased estimates. Although EGARCH model showed characteristics of unbiased estimates during 20 and 30 estimate days, it did not show these characteristics since the period after the financial crisis. According to the analysis results using methods of Davidson and Mackinnon (1981), EGARCH model showed the most excellent prediction performances in the period before the financial crisis. On the contrary, the prediction of EGARCH (5 and 10 days), GARCH (20days) and implied volatility (30days) were during the period after the financial crisis. These results indicate that the qualitative characteristics of each variability are different. In other words, there is not any volatility model which is unique and superior in all the qualitative characteristics. Therefore, it is necessary to choose a model considering qualitative prediction periods and characteristic to be focused on in case of using the volatility model. Limitations of this study is the assumption of the average equation as AR (1) process to presume GARCH model and EGARCH model. The daily rate of return of KOSPI200 index is affected not only by its time series process but other exogenous variables. Accordingly, it is required to examine which effects are made on prediction of variability when estimating conditional volatility by inputting exogenous variables significantly affecting the mean equations of EGARCH model, commitment to estimate the conditional volatility, we need to look at what any change in the predictive power of the volatility.