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The purpose of this paper is to propose an improved reinsurance pricing framework, which includes a crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. A yield restatement approach to account for changing crop mix through time is also demonstrated.

The new crop yield forecasting model is empirically analyzed based on detailed farm-level data from Manitoba, Canada, covering 216 crop varieties from 19,238 farms from 1996 to 2011. As well, corresponding weather data from 30 stations, including daily temperature and precipitation, are considered. Algorithms that combine screening regression, cross-validation and principal component analysis are evaluated for the purpose of achieving efficient dimension reduction and model selection.

The results show that the new yield forecasting model provides significant improvements over the classical regression model, both in terms of in-sample and out-of-sample forecasting abilities.

The empirical analysis is limited to data from the province of Manitoba, Canada, and other regions may show different results.

This research is useful from a risk management perspective for insurers and reinsurers, and the framework may also be used to develop improved weather risk management strategies to help manage adverse weather events.

This is the first paper to integrate a credibility estimator for crop yield forecasting, and develop a closed form reinsurance pricing formula.

The purpose of this paper is to analyze the optimal reinsurance contract structure from the crop insurer's perspective.

A very powerful and flexible empirical‐based reinsurance model is used to analyze the optimal form of the reinsurance treaty. The reinsurance model is calibrated to unique data sets, including private reinsurance experience for Manitoba, and loss cost ratio (LCR) experience for all of Canada, under the assumption of the standard deviation premium principle and conditional tail expectation risk measure.

The Vasicek distribution is found to provide the best statistical fit for the Canadian LCR data, and the empirical reinsurance model stipulates that a layer reinsurance contract structure is optimal, which is consistent with market practice.

While the empirical reinsurance model is able to reproduce the optimal shape of the reinsurance treaty, the model produces some inconsistencies between the implied and observed attachment points. Future research will continue to explore the reinsurance model that will best recover the observed market practice.

Private reinsurance premiums can account for a significant portion of a crop insurer's budget, therefore, this study should be useful for crop insurance companies to achieve efficiencies and improve their risk management.

To the best of the authors' knowledge, this is the first paper to show how a crop insurance firm can optimally select a reinsurance contract structure that minimizes its total risk exposure, considering the total losses retained by the insurer, as well as the reinsurance premium paid to private reinsurers.

The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework.

The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixture distribution is proposed. A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR, and information from the observed data of the individual region/province is integrated with the collective experience of the entire crop reinsurance program in Canada.

A comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR's is more conservative, and provides a more scientific approach to enhance the reinsurance pricing.

Credibility models are in the early stages of application in the area of agriculture insurance, therefore, the credibility models presented in this paper could be verified with data from other geographical regions.

The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks.

This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Bühlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.