此篇論文，使用史坦普指數(S&P 500 index)比較Maheu and Mccurdy (2004)所提出的GARCH-Jump模型及GJR-GARCH-normal模型報酬波動性的預測能力。 並使用三種不同的準確度衡量指標 , MSE, 及P 來檢視此兩模型未來1、5、10、15天預測波動性的準確度。 以五分鐘日內價格估計RV及BV作為預測波動性標的(volatility target)。 此外理論上，RV與BV提供了事後跳躍波動性的估計值。 為檢視跳躍波動性是否影響下期的報酬波動性，我們加入上ㄧ期的跳躍波動性估計值到GJR-GARCH模型，評估加入跳躍波動性估計值是否提高報酬波動性預測的準確度。並比較兩種波動性標的結果是否不同。 結果發現，GARCH-Jump模型及加入上ㄧ期的跳躍波動性估計值的GJR-GARCH模型並沒有提高預測波動性的準確度，且兩種波動性標的結果皆相同。此說明加入Jump變數可能干擾模型預測指數報酬波動性的準確度。 In the thesis, the S&P 500 index is used to compare the accuracy of forecasting volatility by the GARCH-Jump model developed by Maheu and Mccurdy (2004) relative to the benchmark GJR-GARCH model with normal distribution. We use the criteria of , MSE, and P to evaluate the accuracy of forecasting volatility one period into the future, as well as 5-, 10-, and 15-period forecasts. Two volatility targets are calculated by the 5-min prices, realized volatility and bipower volatility. They allow us to obtain theoretical ex post jump measures. Then, we test whether models added the last previous jump measures improve the accuracy of forecasting volatility, which implies that jumps occurred past the period make an effect on future volatility. Finally, we compare results with different volatility targets. We find that the GARCH-Jump model and the models added the last previous jump measures do not provide superior volatility forecasts. The results of two volatility targets are the same. This implies that adding jump component would noise the accuracy of forecasting index volatility.
