The Pricing And Efficiency Of Agricultural Weather Derivatives

There are obvious weather risks in agricultural production in China, which can be devided into catastrophic weather risks and non-catastrophic weather risks. The catastrophic weather risks are hedged by traditional agricultural insurance and government payments. The noncatastrophic weather risks greatly affect agricultural production. However, there are no corresponding methods to hedge against the weather risks, which leave great uncertainty of the agricultural revenue lost of farmers in China. In the international weather risk management market, weather derivatives are widely used to hedge against the noncatastrophic weather risks, and are employed in agricultural production gradually. In recent years, reachers are beginning to study the pricing and application of weather derivatives in agriculture in China. There are four key aspects included in the pricing of weather derivatives: identify the basic weather index, choose proper pricing model, set the strike levels and evaluate the effect of weather derivatives. In this study, the four aspects above will be analyzed accordingly.The study area is located in the Northern spring corn sown area in China. The fractional polynomial model on the relationship between weather indexes and corn yields are constructed to estimate the effects of growing degrees index and precipitation index in order to indentify the basic weather indexes of weather derivative contracts. The fractional polynomial regression is estimated to study the effects of growing degree days and monthly precipitation on corn yields.After indentifying the basic weather indexes, proper models need to be choosen for the pricing of weather derivatives. There are three methods for pricing weather derivatives: burn analysis, index distribution model and the mean revision process model. The basis of the index distribution model and the mean revision process model are historical values and predicting values of the corresponding weather indexes. The mean revision process is for the pricing of temperature related weather derivatives rather than the pricing of precipitation related weather derivatives. Therefore, the methods of index distribution model and mean revision process are compared and evaluated for the pricing of weather derivatives for growing degree days. In estimating the mean revision process, different parameter estimate methods are considered for the mean revision model. The results of the index distribution model and the mean revision model are evaluated and compared to find the most suitable pricing method for the pricing of growing degree days.On the basis of identifying the basic weather index and the proper pricing methods, the effects of strike values on the pricing of weather derivatives are analyzed. In the previous study, the strike value is set as the expected value of the corresponding weather index, which cannot show the effects of strike values on the pricing of weather derivatives. In this study, it is assusmed that the the basic weather index follows a normal distribution, and the strike levels are set to change in a scope given by the expected value and the standard deviation of the weather index. Then, the mathematical relationship between strike levels and the prices of weather derivatives are reflected by the pricing model. Ratios between payoffs and risk lost and between payoffs and option premiums are employed to reflect the effects of applying weather derivative contracts.Results show that the fractional polynomial model can predict the effects of weather indexes on corn yields very well, and there are obvious non-symmetric linear relationship between growing degree days and crop yields. The negative effects of low growing degree days are bigger than that of higher growing degree days. The decrease of growing degree days causes a dramatic drop of corn yields, while the increase of growing degree days results in a slow decrease in corn yields. The goodness of fit of the fractional polynomial model is 80.9%. Using Monte Carlo Simulation to predict corn yields basing on the fractional polynomial model, it is shown that the predicted corn yields are very close to the actural value of the corresponding corn yields.The basis of the pricing of weather derivatives is to estimate the corresponding weather index. In this study, the results of predicting values for weather index is evaluated and compared for the index distribution methods and the mean revision model, which are estimated by three estimation methods. By comparing the mean absolute variations, the accurency of the pricing methods from high to low are listed as follows: index distribution methods, firt order autocorellation mean revision model, seasonality mean revision model, and martingnale estimation function mean revision model and discrete mean revision model. The mean absolute values of the first three models are smaller than the standard deviation of the corresponding weather index, so these three models are suitable for the pricing of weather derivatives.The relationship between strike levels and the prices of the weather index contracts are analyzed according to the probability density function of the weather index. Results show that the prenimums of the weather derivative contracts decrease as the strike values getting higher for call option or lower for put option.When the strike value is far away from the mean of the weather index, the probability that the actual value exceeds the strike level is getting lower, and the the probability that the buyer gets payoffs decrease, so the preminimus is lower, vise vesa. The buyers need to take the relationship of strike values and the prenimus into consideration. In the study of hedging efficiency, based on the indexes that have obvious effects on corn yields, say, options for growing degree days, prepicipation in July, August and September. Results show that under the scenarios of without and with subsidy, it is efficient to apply weather derivatives on growing degree days and rainfall to hedge weather risks in cron production.