動量差：全新的波動度估計式

Abstract

本篇論文提出了一個全新的波動度估計式－動量差，它結合了報酬率和變幅兩種波動度估計式個別的優點，接著我們以GARCH和CARR的模型假設作為基礎，並將上述兩個模型原本的估計式代入動量差提出GARCH-MD和CARR-MD兩種相對應的波動度預測模型，最後選取澳洲普通股指數、德國股市指數、英國金融時報指數、香港恆生指數、日經平均指數和標準普爾500指數六種指數進行樣本外的波動度與風險值(VaR)預測能力的比較，結果顯示本篇論文提出的兩種動量差波動度預測模型在大部分的情況下都比GARCH和CARR模型的預測能力還要好。

This study proposes a new volatility Estimator named momentum deviation which combines the advantages of both return and range measure. We develop two different momentum deviation volatility models called GARCH-MD and CARR-MD based on the Generalized Autoregressive Conditional Heteroskedasticity model (GARCH) and the Conditional Autoregressive Range model (CARR) which allows separate dynamic structures for the positive and negative momentum of assets prices. By using stock market index data including AORD, DAX, FTSE, Heng Seng, Nikkei225 and S&P500, we show that the GARCH-MD and the CARR-MD do provide sharper volatility estimates compared with GARCH and CARR model in our out-of-sample volatility forecasts.