原油價格波動受國際政經影響甚劇，針對原油價格波動進行風險管理已成為投資人的主要課題。由於原油價格與期貨價格可能皆會因稀少事件的發生而存著價格不連續現象。本研究先利用Chan and Young (2006) 提出的雙變量ARJI-GARCH模型捕捉價格不連續的變動及現貨報酬與期貨報酬的共變異數關係。以2010年至2011年美國西德州原油價格為主要研究對象，利用移動視窗(rolling window)法探討樣本外(out of sample)預期不足額，比較未避險模型、雙變量GARCH模型與雙變量ARJI-GARCH模型的最小變異數避險組合之條件預期不足額。研究發現因雙變量ARJI-GARCH模型能捕捉資產間動態波動性、跳躍動態過程與相關跳躍關係，因此估計最小變異數避險組合的條件預期不足額，比起未避險模型與雙變量GARCH模型，有較佳的表現。因此，若僅考慮資產價格間的動態波動性，容易造成投資人承擔超過預期的損失，此結果可為投資人避險的參考。 The fluctuations of the crude oil prices were severely influenced by the international political and economic influence. For the crude oil price volatility, risk management has become the main topics of the investors. For some rare events, the crude oil spot and futures prices are likely to maintain the phenomenon of price jump. In this study, the change of the price jump and the covariance relations of the spot and futures returns are captured by the bivariate ARJI-GARCH model proposed by Chan and Young (2006). The main research object is the spot and futures price of U.S. West Texas Intermediate crude oil in 2010-2011. Using the rolling-window method estimates the out-of-sample expected shortfall. The conditional expected shortfall of the minimum variance hedge portfolio is estimated by three models, unhedge model(GARCH model), bivariate GARCH model and bivariate ARJI-GARCH model. By comparing the estimating results, this study found that the bivariate ARJI-GARCH model estimates the conditional expected shortfall of the minimum variance hedge portfolio owns a better performance, because the bivariate ARJI-GARCH model can capture the dynamic volatility, dynamic jump process and the jump relation between the assets. Therefore, if considering only the dynamic volatility of asset prices, investors will be likely to bear the loss more than expected. This results can be a reference for investors to hedge.
