Abstract: Based on the price of Shanghai copper futures, a three-factor model, including spot price, convenient yield, and stochastic volatility, was proposed. Before constructing the model, the mean-reverting feature of the copper spot price and the convenient yield were examined by using the method of seemingly unrelated regression analysis (SUR) and the features of stochastic volatility were verified by using AR-GARCH model. The analytical solution to the price of futures was obtained. The model was further estimated by using the data from 2010 to 2019, via the state-space model and the extended Kalman filter technique. The results show that the spot price, convenience yield, and volatility are all positively correlated. Besides, the three-factor model can capture the changes in volatility very well, especially in the periods of price slumping and booming. In addition, compared with the classic Schwartz two-factor model, the three-factor model has a much higher fitting accuracy.

Key words: copper futures, three-factor model, stochastic volatility, term structure model

摘要： 基于沪铜的期货价格，构建包含商品现货价格、随机便利收益、随机波动率的三因子模型，对沪铜期货进行定价研究。使用似无关回归分析（SUR）方法，检验了沪铜现货价格和便利收益具有均值回复的特征，同时检验了库存理论的有效性；利用AR-GARCH模型检验了不同期限的铜期货价格具有随机波动率的特征。最后，提出三因子模型的构建方式，推导得出期货定价公式的解析解，并结合状态空间模型和扩展卡尔曼滤波对模型进行估计。使用2010~2019年的沪铜期货价格进行实证研究，结果表明：铜现货价格、便利收益与随机波动率间均呈正相关；模型在样本期内拟合效果较好，尤其在2012年铜期货暴跌与2017年铜期货暴涨的时段内，三因子模型能够很好地捕捉到波动率的变化。此外，相比于经典的Schwartz双因子模型，本文提出的三因子模型具有更高的拟合精度。

关键词: 铜期货, 三因子模型, 随机波动率, 期限结构模型