변동성 모형의 질적 특성에 관한 연구 (A Study on the Quality of Volatility Models)

서지정보

· 발행기관 : 한국기업경영학회
· 수록지 정보 : 기업경영연구 / 19권 / 6호 / 257 ~ 281페이지
· 저자명 : 안주영, 김철중

초록

본 연구의 목적은 다양한 분석 방법을 도입한 변동성 모형의 질적 특성 비교하고 평가하는 것을 목표로 한다. 표본자료는 1997년 7월 7일부터 2011년 6월 9일까지의 KOSPI200지수 일별수익률 3509개이며 비교할 모형은 GARCH, EGARCH, EWMA 및 내재변동성 모형이다. 실증분석 결과 예측오차 분석에서는 RMSE 기준으로 비교할 경우 5일, 10일 예측기간은 EGARCH 모형, 20일, 30일 예측기간은 GARCH 모형의 예측오차가 가장 작다. MAE 기준으로 비교할 경우 5일 예측기간은 EGARCH 모형, 10일 예측기간은 EWMA 모형, 20일, 30일 예측기간은 GARCH 모형의 예측오차가 가장 작은 것으로 나타났다. MAPE 기준으로 비교할 경우 모든 예측기간에서 EWMA 모형이 가장 우월한 예측력을 보였다. 정보효과 분석에서는 20일의 예측기간은 내재변동성모형이, 5일과 10일 그리고 30일의 예측기간은 EGARCH 모형이 우월한 것으로 나타났다. 불편성 분석한 결과, EWMA 모형이 10일, 20일, 30일의 예측기간에서 불편성을 갖는 것으로 나타났다. 모형의 직관적 비교가 가능한 Davidson and Mackinnon(1981)의 방법론을 이용하여 변동성 모형을 분석할 경우 5일과 10일 예측기간에서는 EGARCH 모형이, 20일과 30일 예측기간에서는 GARCH 모형이 우월한 예측력을 갖는 것으로 나타났다. 글로벌 금융위기 전후 기간에 대해 Davidson and Mackinnon(1981)의 경합모형 분석 방법을 적용할 경우 금융위기 이전에는 EGARCH 모형이, 반면에 금융위기 이후에는 EGARCH(5일, 10일), GARCH(20일), 내재변동성(30일)의 예측력이 우수한 것으로 분석되었다. 이러한 결과는 각 변동성 모형이 갖는 질적 특성이 다르다는 것을 나타낸다. 즉, 모든 질적 특성에서 가장 우월하고 유일한 변동성 모형은 존재하지 않는것을 나타내는 것이다. 따라서 변동성 모형을 이용할 경우 예측하려는 기간이나 집중하고자 하는 질적 특성을 고려하여 모형을 선별할 필요가 있다

영어초록

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.

참고자료

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