Modeling Frost Losses: Application to Pricing Frost Insurances

The main objective of this paper is to model the losses caused by frost events and use it to price frost insurances. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damages. The main challenges in modeling frost loss variables are first, the non-linearity of the frost losses with respect to the temperature and second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurances for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk and Wang's premium based on temperature data from San Joaquin Drainage County in California.