Hedging the Effect of Climate Change on Crop Yields by Pricing Weather Index Insurance Based on Temperature

In this paper, we calculate the premium of weather index insurance written on temperature indices. To model the daily average temperature data, we use a stochastic model in which the noise part is determined by a generalized hyperbolic process. We used daily data recorded in two cities in Ethiopia to validate our model. A growing degree day (GDD) temperature index is employed for calculating the price of index insurance that is used to hedge the loss of crop yields associated with an abrupt change of temperature. Using the GDD index, we calculate the premium of the insurance contract used to ensure three major crops, namely teff, wheat, and barley. Moreover, the risk factor of weather derivative market is calculated from the historical temperature data by calculating the GDD which is the highlight of the paper. Depending on the method implemented, the calculated value of the market price of risk is 0.028, with the corresponding premium value of 290. This premium value is more accurate than the value obtained assuming that, the market price of risk is zero. We have also proposed a normal distribution to model payoff movement of an insurance contract, and we are studying the probability of profit and loss for the farmer who enters the insurance. Our results are promising for establishing weather index insurance.