Applications of Copulas to Analysis of Efficiency of Weather Derivatives as Primary Crop Insurance Instruments

Abstract

Numerous authors note failure of private insurance markets to provide affordable and comprehensive crop insurance. Economic logic suggests that index contracts potentially may have some advantages when compared with traditional (farm based) crop insurance. It is also a matter of common knowledge that weather is an important production factor and at the same time one of the greatest sources of risk in agriculture. Hence introduction of crop insurance contracts, based on weather indexes, might be a reasonable approach to mitigate problems, associated with traditional crop insurance products, and possibly lower the cost of insurance for end users. In spite of the fact that before the financial crisis of 2008-09 market for weather derivatives was the fastest growing derivatives market in the USA, agricultural producers didn’t express much interest in application of weather derivatives to management of their systematic risk. There are several reasons for that, but the most important one is the presence of high basis risk, which is represented by its two major components: technological (i.e. goodness of fit between yield and weather index) and geographical basis. Majority of the researchers is focusing either on pricing of weather derivatives or on mitigation of geographical basis risk. At the same time the number of papers researching possible ways to decrease technological basis is quite limited, and always assumes linear dependency between yields and weather variables, while estimating the risk reducing efficiency of weather contracts, which is obviously large deviation from reality. The objective of this study is to estimate the risk reducing efficiency of crop insurance contracts, based on weather derivatives (indexes) in the state of Texas. The distributions of representative farmer’s profits with the proposed contracts are compared to the distributions of profits without a contract. This is done to demonstrate the risk mitigating effect of the proposed contracts. Moreover the study will try to account for a more complex dependency structures between yields and weather variables through usage of copulas, while constructing joint distribution of yields and weather data. Selection of the optimal copula will be implemented in the out-of-sample efficient framework. An effort will be done to identify the most relevant periods of year, when weather has the most significant influence on crop yields, which should be included in the model, and to discover the most effective copula to model joint weather/yield risk. Results suggest that effective insurance of crop yields in the state of Texas by the means of proposed weather derivatives is possible. Besides, usage of data-mining techniques allows for more accurate selection of the time periods to be included in the model than ad hoc procedure previously used in the literature. Finally selection of optimal copula for modeling of joint weather/yield distribution should be crop and county specific, while in general Clayton and Frank copula of Archimedean copula family provide the best out-of-sample metric results.