在經濟與財務的理論與實務中,風險問題愈來愈受重視,故如何將風險納入實證模型中,就顯得相當地重要。台灣對美國的經濟依存度相當的高,美國股價指數的風險經常直接或間接地影響台灣金融商品價格變動。因此,本研究藉由評估美國股價指數市場的風險,以作為國內投資者規避因投資與美國股價指數市場連動性高的相關資產時所承擔風險的依據。 實證上以美國道瓊工業指數、S&P 500指數與Nasdaq股價指數為研究對象,利用蒙地卡羅模擬法衡量歷史波動與隱含波動,以及由GARCH及GAIV模型所求算之波動率,並將其應用在不同市場且不同模型下風險的衡量。實證期間介於2005年10月6日至2007年7月31日,並分別採用樣本外預測30天期的未來波動,再利用RMSE、MSE、MAPE和Theil’U等四種預測力指標,針對四種波動預測模型進行比較和分析。 由衡量誤差的指標可發現,IV和GARCH模型在經由蒙地卡羅模擬其波動的路徑後,可得到最適合描述美國股價指數市場風險的模型,且IV模型的預測能力相對於GARCHMC模型更為準確。此外, IV和GARCHMC模型可以有效地預測股價指數市場劇烈的波動。
Recently, the risk problem, faced by investors and managers, has received the attention of the economic and financial researchers. They try to construct different kinds of risk evaluation models to measure the risks. Because Taiwan economic development and export trade highly depend on US economy growth, the risks derived from the stock market in American would deeply influence the returns and risks in Taiwan’s financial markets. Therefore, this research attempts to adopt different risk measure models to calculate the value at risk of American stock market, and by employing the estimated VaR Taiwan’s investor can avoid the risks stemmed from holding the assets that have high correlation with American stock index market. In empirical study we choose DJIA, NASDAQ and S&P500 in American stock market as sample objects, and use Monte Carlo simulations to simulate the error of Historical volatility, implied volatility (IV), GARCHMC (GARCH combined with Monte Carlo simulation) and GAIV (GARCH combined with IV) models and evaluate the VaR. Sample period spans from Oct, 2005 to Oct, 2008. Moreover, to evaluate their forecasting performance we use four different measure methods, including the mean absolute errors (MAE), mean absolute percentage errors (MAPE), root mean squared errors (RMSE) and Theil’s Inequality Coefficient (Theil’U). Empirical result shows that the IV and GARCHMC models all have the best forecasting performance in VaR, but IV has better individual forecasts than GARCHMC model. Finally, IV and GARCHMC are efficient to forecast violent volatility of the stock markets.