摘要
In this paper we present a stochastic model for daily average temperature to calculate the temperature indices upon which temperature-based derivatives are written. We propose a seasonal mean and volatility model that describes the daily average temperature behavior using the mean-reverting Ornstein-Uhlenbeck process. We also use higher order continuous-time autoregressive process with lag 3 for modeling the time evolution of the temperatures after removing trend and seasonality. Our model is fitted to 11 years of data recorded, in the period 1 January 2005 to 31 December 2015, Bahir Dar, Ethiopia, obtained from Ethiopia National Meteorological Services Agency. The analytical approximation formulas are used to price heating degree days(HDD) and cooling degree days(CDD) futures. The suggested model is analytically tractable for derivation of explicit prices for CDD and HDD futures and option. The price of the CDD future is calculated, using analytical approximation formulas. Numerical examples are presented to indicate the accuracy of the method. The results show that our model performs better to predict CDD indices.
本文提出了一个基于温度的导数来计算温度指数的日平均温度随机模型,该模型提出了一个季节性均值及其波动率的计算方法,使用均值回归的Ornstein-Uhlenbeck过程来刻画日平均温度的变化。本文还采用连续的三阶自回归过程来模拟去除趋势和季节性影响后的温度演变过程,模型的模拟结果与从埃塞俄比亚国家气象厅获得的2005年1月1日至2015年12月31日11年间埃塞俄比亚Bahir Dar记录的数据非常吻合。验证后的近似公式很容易根据热日和冷日(heating degree days (HDD) and cooling degree days (CDD))等典型温度指数推导期货价格,也给出了数值例子来说明该方法的准确性。结果表明,本文提出的模型比其他模型能更好地预测CDD指数。