带有随机汇率因素的三因子期货价格的研究

引入随机跳跃的汇率因素,首次建立了跳跃扩散过程的标的资产、便利收益和汇率的三因子期货模型,然后推导出期货价格走势满足的偏微分方程,并求出该偏微分方程的解析解,应用加权最小二乘方法,给出辨识该解析解参数的方法,最后针对中国上海期货交易市场,选取燃料油期货的实际例子,求出了具体的参数并预测了未来的走势.预测结果与真实价格的比较证实了三因子期货模型是精确的,最大相对误差仅为3.772%.

Research on futures price with stochastic exchange rate based on three factors

Considering stochastic exchange rate, a three-factor futures price model was developed with underlying asset, convenience yield and exchange rate. These factors follow jump-diffusion processes. The corresponding partial differential equation (PDE) of the futures price was derived, and its analytical solution was presented. A weight least squares approach was applied to obtain the parameters of the analytical solution. A fuel futures case in Shanghai exchange market was selected to illustrate the above model and method. The comparison between real-time price and forcasting results show that the three-factor futures price model is accurate, and the maximum relative error is 3.772%.