The Time-varying Mean-reverting Model of Forecasting Temperature in Weather Derivatives
The purpose of weather derivatives is to allow businesses and other organizations,which are affected by the weather,to insure themselves against weather changes.Most of researches about weather derivatives mainly focus on temperature derivatives based on HDD and CDD indices.Hence,forecasting the trend of temperature accurately is critical to pricing the weather derivatives.Therefore,this paper mainly studies the forecasting temperature in pricing weather derivatives.In the first part,we give a short overview of weather derivatives including their concepts,the application prospects and the research trend.We further summarize recent studies using the O-U mean-reverting model to price temperature derivatives.The previous studies based on the O-U mean-reverting model considered the mean-reverting speed to be a fixed constant.However,in real life human activity,solar activity,atmospheric changes and other factors will have impact on the climate,thereby affecting the temperature mean-reverting effect.To forecast the change of the temperature more accurately,we considered the mean-reverting speed to change over time.Therefore,this paper proposes a new forecasting temperature model which is called Time-varying mean-reverting model based on the O-U process.The unknown parameters in the model are estimated using historical temperature data.Since we only have discrete observations,the estimation of mean-reverting speed in the model is based on the use of martingale estimation functions.The quadratic variation of the temperature's volatility varies across different months of the year,but nearly constant within each month.In the second part,to obtain the characteristic of the mean-reverting speed we analyzed the data in each year from 1951 to 2011 collected from China's main cities,including Nanjing,Hangzhou,Wuhan and Beijing.The ADF test of Wuhan and Hangzhou shows that their annual mean-reverting speed sequences are stationary series,and can be further treated as white noise sequence.After firstorder difference processing,Beijing and Wuhan's annual mean-reverting sequence turns out to be stationary series,further modeled by AR (2) and ARMA (1,2) according to the AIC criterion of Schwarz criteria,parameters significantly test,and the white noise test for residuals.With the same analysis method,the annual mean-reverting speed in Chinese main cities can be modeled by ARIMA timeseries with different orders.In the third part,we compared our model with the O-U mean-reverting process to forecast the temperature of the main cities in 2011 based on the data from 1951 to 2010.According to the measure error covariance which measures the non-systematic errors,timevarying mean-reverting model is superior to the O-U mean-reverting process.According to the correlation coefficient of the meanreverting sequence between two related cities in Nanjing,Hangzhou,Wuhan and Beijing,we can conclude that the trend of meanreverting within the same latitude is similar.Therefore,we confirm that the time-varying mean-reverting model is applicable in most areas of China.In summary,the temperature prediction model in this paper can reflect Chinese actual situations.Therefore,it can provide suggestions for the development of weather derivatives in China.Furthermore,the time-varying mean-reverting model could be used to forecast the temperature more accurately so that the pricing model about the temperature derivatives can better reflect the reality.
weather derivativesO-U mean-reverting modelTime-varying mean-reverting modelARIMA time-series model
国家科技期刊平台
NSTL
万方数据
维普
