Crop Yield Expectation Stochastic Process with Beta Distribution as Limit, A

David A. Hennessy
November 2009  [09-WP 501]

The modeling of price risk in the theory and practice of commodity risk management has been developed far beyond that of crop yield risk. This is in large part due to the use of plausible stochastic price processes. We use the Pólya urn to identify and develop a model of the crop yield expectation stochastic process over a growing season. The process allows a role for agronomic events, such as growing degree days. The model is internally consistent in adhering to the martingale property. The limiting distribution is the beta, commonly used in yield modeling. By applying binomial tree analysis, we show how to use the framework to study hedging decisions and crop valuation.

Keywords: crop insurance, growing degree days, martingale, Pólya urn, stochastic process.

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