A cointegrated commodity pricing model
提出了一个扩展Gibson-Schwartz两因子模型的商品定价模型，纳入商品现货价格间的线性关系（协整），推导出期货和看涨期权价格，并用原油和取暖油数据估计模型，应用于短期期货对冲长期期货。
We propose a commodity pricing model that extends the Gibson–Schwartz two‐factor model to incorporate the effect of linear relations among commodity spot prices, and provide a condition under which such linear relations represent cointegration. We derive futures and call option prices for the proposed model, and indicate that, unlike in Duan and Pliska (2004), the linear relations among commodity prices should affect commodity derivative prices, even when the volatilities of commodity returns are constant. Using crude oil and heating oil market data, we estimate the model and apply the results to the hedging of long‐term futures using short‐term ones.