金融市場瞬息萬變，若能更確切地捕捉資產價格波動的特性，將有助於投資組合配置的最適化，進而能有效地控制風險，帶給投資人更多的助益。目前在波動性預測模型中被應用最廣泛的是ARCH/GARCH族，而且在實證上也獲得相當不錯的成效。本文採用Chou(2005)CARR模型驗證在黃金現貨價格及那斯達克股價指數上是否改善波動性的預測能力。 第一部份以黃金現貨價格、那斯達克股價指數為研究對象，分別進行CARR模型和GARCH模型樣本外波動性預測能力之比較。第二部份以有平均數的GARCH模型、AR(1)-GARCH模型及GARCH-M(GARCH in Mean)模型進行比較，檢視何者為最佳波動性預測模型。實證結果顯示，以那斯達克股價指數為研究標的時，CARR模型的樣本外預測能力較佳。 Volatility plays an important role in finance. If we can capture the characteristics of the motions of assets precisely, we could make good portfolios and control risks efficiently. GARCH models have been used in the forecast of volatilities generally, and performed well in many empirical studies. However, Chou(2005) proposed the CARR model and compared in the CARR model and traditional GARCH model based on the data of S&P 500 index. CARR is better in the volatility forecasting. This paper tests and verifies the forecasting power of the CARR model based on the Gold price and the stock price index of NASDAQ. We choose the Gold price and the stock price index of NASDAQ to compare the CARR and GARCH models in out-of-sample forecast. And then we apply GARCH, GARCH-M and AR(1)-GARCH models to test which model is the best. Our empirical results show that the CARR model is preferable to the GARCH model only in the data of NASDAQ.
