Weather Index Insurance Design Based On Copula Method

Weather index insurance is an innovation in agricultural insurance in recent years,and it is considered to be promising to fill some of the shortcomings of traditional crop insurance.The main advantage of weather index insurance is to alleviate information asymmetry problems related to adverse selection and moral hazard,and it is an effective means to transfer agricultural production risks,prevent and mitigate disasters and improve post-disaster recovery,especially in the case of extreme weather events.However,due to the existence of basis risk,it is difficult to promote weather index insurance.In order to improve the effectiveness of weather index insurance and enhance farmers’ willingness to take out insurance,this paper introduces the Copula function to construct the relationship between weather index and yield based on previous studies,and uses the conditional yield distribution function derived from the Copula function to determine the insurance rate so as to reduce the basis difference risk of weather index insurance as much as possible.Specifically,based on the rice yield,temperature,rainfall and sunshine hours data in Jiamusi City,Heilongjiang Province during 1989-2019,this paper first uses the moving average method to de-trend the rice yield and strip out the weather yield,then determines the weather index affecting the weather yield in Jiamusi City based on the moving average correlation results,and finally selects the rainfall as the optimal weather index for rice weather index insurance in Jiamusi City.After obtaining the optimal weather index and weather yield,the optimal marginal distribution function of weather index is first fitted from P-III distribution,Gamma distribution,GEV(generalized extreme value)distribution,normal distribution,log-normal distribution,and then from P-III distribution,GEV(generalized extreme value)distribution,normal distribution,log-logistic distribution,student-The optimal marginal distribution function of weather yield is then fitted from P-III distribution,GEV(generalized extreme value)distribution,normal distribution,log-logistic distribution,and student-t distribution.Based on the fitted optimal edge distribution function,the Copula function was fitted and the AIC information criterion and Euclidean square distance were used as the judgment criteria for the optimal Copula,and finally the Rotated270 Gumbel Copula with upper tail correlation was selected as the optimal Copula function.Finally,based on the Rotated 270 Gumbel Copula,the weather index insurance of Jiamusi City is designed and the insurance premium rate is derived.In order to enhance the accuracy and universality of weather index insurance,this paper has designed weather index insurance specifically for extreme events.Because this has the following four benefits: first,extreme weather events require more timely financial relief,and weather index insurance payouts based on the index are more advantageous under extreme events;second,the greater spatial dependence of extreme weather time reduces the spatial basis risk due to weather station location deviations;third,locking the basis risk at the high level of the weather index reduces the design basis risk range;fourth,it reduces the rate of weather index insurance,which is expected to enhance farmers’ demand for weather index insurance.The results of the study show that the insurance pricing using conditional Copula distribution and marginal expected yield(MES)yielded catastrophe weather index insurance premium rates of 1.7166%,1.6124% and 1.1990% for Jiamusi,which correspond to catastrophe coverage levels of weather indices exceeding their quartiles of 0.7,0.8 and 0.9,respectively.Finally,this paper proposes policy recommendations in four aspects:monitoring of weather data,design of insurance products,support and guidance of index insurance,and establishment of insurance apportionment mechanism.