Measuring Price Risk in Rating Revenue Coverage: BS or No BS?

The Black-Scholes (BS) option pricing model has been a cornerstone of modern financial theories since its introduction by Black and Scholes (1973) and its subsequent refinement by Merton (1973). The model has realized widespread adoption for a number of purposes. Inherent in the model are a number of assumptions. An important and potentially restrictive assumption is that the underlying asset price is log–normally distributed. Among the many diverse uses of the BS model, the model and underlying theory are used to derive measurements of the variance of expected (harvest-time) prices for use in rating revenue coverage in the federal crop insurance program. Revenue coverage currently accounts for about 80% of the total liability insured in the program. This liability frequently exceeds $100 billion and thus the accuracy of revenue premium rates is of vital importance. The use of the BS model by the Risk Management Agency (RMA) of the USDA has been the focus of recent criticisms of the program. Critics have argued in favor of retrospective measures of price variability that are based on historical price movements or have recommended other approaches to measuring price risk. This article reports on a contracted review of revenue insurance rating methodology commissioned by RMA. We evaluate a number of alternative approaches to measuring expected price variability, including several approaches recommended by critics of the federal program. Our results suggest that the BS model is preferred to recommended alternatives on the basis of numerous criteria.