臺灣博碩士論文加值系統

本文研究首先彙整民國96年至民國98年間台灣股價指數期貨資料並且利用ARMA(1，1)-GJR(1)-GARCH(1，1)模型建立條件波動預測值，另外也收集VIX波動度指數資料作為引含波動度代理模型，並同時將兩種模型分別對於不同資料頻率下所產生的真實波動度進行迴歸分析以及利用MAE、RMSE、MAPE等衡量指標進行績效診斷。

接著本研究探討GJR-GARCH模型預估值與真實選擇市場所反推之隱含波動度之間是否因投資者心理因素改變而存在差距，並針對此現象嘗試著提出波動度套利的操作策略，並判斷此一策略是否會帶來套利利潤。最後針對GJR-GARCH模型提出修正，提升模型對於真實市場隱含波動度的補捉能力。
實證分析結果如下：
首先研究結論指出GJR-GARCH模型對於真實波動度並無顯著的解釋能力，而VIX隱含波動度指標對於真實波動度有正的顯著影響存在。此外在不同的資料頻率下所計算之真實波動度對於實證結果並無顯著的影響。再者台灣期貨市場存在著不對稱效果，投資者對於市場上所釋放出來的好壞消息解讀並不相同，尤其以壞消息所造成的波動度加劇較為明顯。另外由於選擇權市場存在著每個月交割結算滴恐慌效應，此一效應透過Delta hedge的套利操作策略將替套利投資者帶來超額報酬。最後GJR-GARCH模型預測值必須透過模型修正才能捕捉選擇權市場具有每月到期交割的特性，藉以提升對於市場選擇權隱含波動的預估能力。

Volalitity is not only the key factor to determine the price of assets but also the risky index of underlying assets. There are many volatility farecasting models and none of them are perfect. To compare the performance of these model, this study uses 2007 to 2009 TAIEX futures data to construct three volatility forecast models, which are historical volatility, time series volatility, and implid volatility model. Base on the MAE, RMSE and MAPE criterions. we find that VIX combine GJR-GARCH model performs well in forcasting volatility. This implies the leverage effect do exist in the Taiwan stock market and futures market.

This study also tries to find the gap between GJR-GARCH Model and impled volatility. First the GJR-GARCH volatility and implied volatility almost move together in most of the days. However, when the day near the delivery date of options, the impled volatility jump up suddenly and the closer to the delivery date, the larger gap between these two volatilities. The intuition behind this is due to the worry of a suddenly shock before delivery date will encourge options writers to ask for higher premium to compensate the risk of volatility shock. Furthermore, the implied volatility of put is always greater than that of call options. This implied that the investors are more afraid of down side risk than up side risk. Knowning this fact, this study constructs a volatility forecasting model by adding dummy variables to count the near-delivery-date effect. This model outperforms other volatility models in forecasting the options prices.