天气衍生品作为一种规避天气风险的金融衍生品,如何对其准确定价一直以来是学术界争论的焦点。文章以Alaton[5]提出的基于月波动率的O-U模型为基础,将原模型中的常量均值回复速率考虑为随时间变化的变量,并通过ARMA(p, q)模型分析该时间序列的变化规律,进而建立时变O-U模型。基于北京市自1951年以来的日平均气温数据,分别模拟了2010-2012共计三年的日平均气温,并与其真实值对比发现:改进后的模型残差平方和更小,而偏差比例、方差比例和协方差比例也显示改进后的模型对温度预测效果更好。最后,基于北京市的数据通过蒙特卡洛仿真计算了CDDs和HDDs,并进行了相关的期货合约定价,进一步验证了改进后模型的适应性。
How to accurately price the weather derivatives,which as a sort of weather risk-hedging financial derivatives, has always been the focus of academic debate. Based on the O-U model of monthly volatility presented by Alaton[5], the speed of mean reversion is considered in this paper,which is a constant in the original model as a time-dependent variable. Then the time sequence of the speed of mean reversion is analyied by ARMA(p, q) model and establish the time-varying O-U model. Based on Beijing's daily average temperature data from 1951, three years of daily average temperature from 2010 to 2012 are simulated respectirely, and compared with its true value. After the comparison,it is found that: the residual sum of squares of the improved model are smaller, meanwhile the bias proportion, the variance proportion and the covariance proportion also show the improved model obtains a better temperature prediction. Finally, the CDDs are calculated and HDDs are calculated according to Beijing's daily average temperature data by Monte Carlo simulation, and then price the related futures contract to further validate the adaptability of improved model.
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