銅價在近年來不斷的創下歷史新高，由於台灣蓬勃的電子、半導體、工具機產業皆需要銅，因此銅進口量位居全球第五(ICSG,2009)，使得台灣企業的生產成本受國際銅價的波動影響甚鉅，全球有70%的銅價是按照英國倫敦金屬交易所(London Metal Exchange, LME)的牌價進行貿易，因此本研究欲建置預測模式以預測銅價未來趨勢。 　　本研究之資料來源為2003年1月2日至2011年7月14日的LME三月期銅價，並依文獻探討選取LME的銅庫存、三月期鋁價、三月期鉛價、三月期鎳價、三月期鋅價、三月期錫價，以及金價、銀價、石油價格、美國生產者物價指數、美國消費者物價指數、聯邦資金利率作為影響因素的分析資料。時間序列分析、類神經網路已被廣泛的用於預測股市及期貨，本研究先藉由向量自我迴歸模型篩選出有影響力的變數，同時建置GARCH時間序列預測模型與具有遞迴的Elman類神經網路預測模型，再整合兩者建置GARCH-Elman類神經網路預測模型。 本研究之向量自我迴歸模型顯示銅價與金、鋁、銅庫存前第1期；自身前第2期；鎳、錫前第3期；鋅前第4期的變動有負向的影響；受到石油前第2期的變動有正向的影響，這其中以銅的自我解釋變異最高，銅庫存最低，推測其影響已有效率地反映到銅價上。也驗證預測模型必須考量總體經濟變數，且變數先經向量自我迴歸模型的篩選能因減少雜訊而提升類神經網路的預測能力。依此建置的GARCH模型有33.81%的累積報酬率、Elman類神經網路38.11%、整合兩者的GARCH-Elman類神經網路56.46%，皆優於實際銅價指數的累積報酬率。對銅有需求的企業者，能更為準確的預測漲跌趨勢，依此判斷如何跟原物料供應商簽訂合約的價格與期間，使其免於價格趨勢的誤判而提高生產成本，並提出五點建議供未來研究者參考。 / The recent copper price in London Metal Exchange (LME) has breaking the historical high. Taiwan’s booming electronics, semiconductor and machine tool industry causing copper import volume ranked fifth in the world (ICSG, 2009). Because of 70% of copper worldwide trade in accordance with the price of the London Metal Exchange, this study using time series and neural networks to build the LME copper price forecast model. 　　This study considering copper, copper stocks, aluminum, lead, nickel, zinc, tin, gold, silver, oil ,federal funds rate, CPI and PPI during the period of 2003/1/2 to 2011/7/14. Time series model and neural networks have been widely used for forecasting the stock market and futures. In this study, using Vector Autoregressive (VAR) model screened influential variables, building GARCH model and Elman neural network to forecast the LME copper price; and further, integrating this two models to build GARCH-Elman neural network prediction model. 　　This study’s VAR models show that the copper has negative effect with gold, aluminum, copper stocks, nickel, tin, zinc and itself. And has positive impact with oil prices. The highest of explained variance is copper. Copper stocks are lowest, speculating that its impact has been efficiently reflecting on the price of copper. Verifying the prediction model must consider the macroeconomics variables. Using VAR model screened influential variables can reduce noise to enhance the predictive ability of the neural network. This study’s GARCH model has 33.81% of the cumulative rate of return, Elman neural network has 38.11% and the GARCH-Elman neural network has 56.46%. All of them are better than the actual price of copper.

本文係針對臺灣50指數期貨與基金於2003年6月30日上市之後，臺灣期貨及現貨市場報酬率間領先落後關係與波動性的變化來進行探討。研究分為兩部份，第一部份是觀察臺灣50指數期貨與現貨之間的關聯性，並探討臺灣加權股價指數、金融保險類股股價指數及電子類股股價指數期貨與現貨市場間的變化；第二部份是採用可模擬現貨走勢的臺灣50指數基金、國泰金及臺積電的股價來做為現貨的替代變數，觀察其與期貨之間的關連性是否與第一部份的結果類似，若是實證結果極為相同，則相關機構與一般投資人將可運用各期貨與其標的指數中市值最大的股票來進行套利操作。此外，本文在進行模型估計時，首度採用一階段估計法，來聯合估計雙變量GARCH模型中的條件平均數方程式與條件變異數方程式，以避免過去相關文獻將兩條方程式個別估計時所造成的估計誤差。 實證結果所獲得的重要結論如下：首先，臺灣期貨市場的發展仍未趨成熟，並不具有價格發現的功能，在考慮風險溢酬方面，僅有臺灣50指數期貨與現貨的投資人會在報酬率之外，額外要求用以補償的風險溢酬，再者，臺灣50指數期貨與基金的上市，並沒有對臺灣現有的期貨與現貨市場造成顯著的影響，然而，替代變數並不能完全取代現貨指數，但相較之下，國泰金在臺灣50指數期貨與基金上市之後的那段期間模擬成效最好。 / This paper investigates the change of lead-lag relationship in returns and volatilities in Taiwan futures and spot markets after the introduction of Taiwan 50 Futures and Taiwan Top50 Tracker Fund (TTT) on June 30, 2003. The study divides into two parts. The first part examines the relationship between Taiwan 50 Futures and spot markets, and also discusses the change of Taiwan Stock Exchange Capitalization Weighted Stock Index, Taiwan Stock Exchange Banking and Insurance Sector Index, and Taiwan Stock Exchange Electronic Sector Index in futures and spot markets. Another part uses the stock price of TTT, Cathay Financial Holding Company and Taiwan Semiconductor Manufacturing Company as the substitutive variables of spot index and goes a step further to examine the relationships between them and futures individually. Additionally, this research used One-Pass Method for first time to estimate jointly the conditional mean equation and conditional variance equation of Bivariate GARCH Model to avoid estimating error in previous relative studies with Two-Pass Method. The major empirical results are as follows: first, the development of Taiwan futures market is incomplete. The futures market does not play the price discovery role to the spot market. Second, under the consideration of risk premium, only investors in Taiwan 50 Futures and spot markets would ask for compensated risk premium excepting returns. Third, the opening of Taiwan 50 Futures and TTT does not influence significantly Taiwan futures and spot markets. Last but not least, these substitutive variables can not replace spot index perfectly. However, comparing with others, the stock price of Cathay Financial Holding Company is the very model of Taiwan Stock Exchange Banking and Insurance Sector Index after the introduction of Taiwan 50 Futures and TTT.

附最低保證投資型保險商品的特色在於無論投資者的投資績效好壞，保險金額皆享有一最低投資保證，過去關於此類商品的研究皆假設標的資產為單一資產，或依固定比例之投資組合，並沒有考慮到投資人自行配置投資組合的效果，但大部分市售商品中，投資人可以自行配置投資標，此情況之下，保險公司如何衡量適當的保證成本即為一相當重要之課題。 本研究假設投資人風險偏好服從冪次效用函數，並假設與保單所連結之投資標的有兩種資產，一為具有高風險高報酬的資產，另一為具有低風險低報酬之資產，在每個保單年度之初，投資人可以選擇配置在兩種資產之比例，我們運用黃迪揚(2009)所提出的動態規劃數值解之方法，計算出在考慮投資人自行配置資產之下，保證成本將會比固定比例之投資高出12個百分點。 此外，為了瞭解在不同資產報酬率的模型之下，保證成本是否會有不一樣的結論，除了對數常態模型之外，我們假設高風險資產與低風險資產服從ARIMA-GARCH(Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedastic )模型，並得到較高的保證成本。 / The main characteristic of variable annuities (VA) with minimum benefits is that the benefit will be guaranteed. Previous literatures assume a specific underling asset return process when considering the guaranteed cost of VA; but they do not consider the portfolio choice opportunity of the policyholders. However, it is common for policyholders to rebalance his portfolio in many types of VA products. Therefore it’s important for insurance companies to apply an approximate method to measure the guaranteed cost. In this research, we assume that there are two potential assets in policyholders’ portfolio; one with high risk and high return and the other one with low risk and low return. The utility function of the policyholder is assumed to follow a power utility. We consider the asset allocation effect on the guaranteed cost for a VA with guaranteed minimum withdrawal benefits, finding that the guaranteed cost will increase 12% compared with a specific underling asset. The model effect of the asset return process is also examined by considering two different asset processes, the lognormal model and ARIMA-GARCH model. The solution of dynamic programming problem is solved by the numerical approach proposed by Huang (2009). Finally we get the conclusion which the guaranteed cost given by the ARIMA-GARCH model is greater than the lognormal model.