Barry Goodwin, Ardian Harri, Rod Rejesus and I just published a paper in the American Journal of Agricultural Economics examining the use of the Black-Scholes implied volatilities in rating crop revenue insurance. For those not familiar with futures option implied volatility, it is derived from observed option premiums and known parameters of the option contract. Under certain assumptions it is the price volatility implied by the price of the option contract.
To rate a revenue contract one needs both an expected price and a volatility associated with that expected price. Needing an expected price is rather obvious, but many forget that the price volatility estimate profoundly affects premium rates. In 2017 the premium associated with these revenue insurance policies was approximately $7.68 billion dollars. Just a few years ago both expected corn and soybean prices and volatilities were much higher than today. For example, in 2010 the price volatility used by the USDA Risk Management Agency (RMA) for Midwest corn was 0.28 while in 2017 it was 0.19. This decline in volatility has reduced premium rates and the amount of subsidy in the program.
Current USDA RMA methods are based upon a pre-signup average of futures closings and Black–Scholes (BS) implied volatilities calculated from “near–to–the–money” options for the harvest time contracts. We focus on options and futures markets during the period of time used by RMA for price discovery (i.e., planting and harvest time pricing).
We find that the Black-Scholes model works well when there is robust trading during the pricing period. We also conclude there is strong support for using a forward looking implied volatility rather than a backward looking historical based volatility. We also determine there is merit in using a third party source of volatility rather than some less transparent model. However, the contracts for which significant violations of the assumptions inherent in the BS model tend to be for thinly traded crops.
This leads to a really interesting question. Does crop revenue insurance which protects against low prices, as well as, low yields reduce the number of natural pre-season hedgers in the futures and options market? If so we have something of a catch-22.
I know that up-side price protection makes revenue insurance more conducive to pre-harvest hedging than straight revenue insurance. But is does also have a substitution effect (Coble, Heifner, Zuniga JARE 2000). In the end I think the prima facie evidence is that corn and soybeans have had robust preseason price data and these two crops have among the highest levels of crop revenue protection insurance participation. Conversely, rice arguably has had the most severe price data problems and yet has relatively low crop insurance participation. Finally, note also that crop insurance does not affect the natural longs in the market. However, we are left with the question of how to utilize the data from a thin market such as rice.
Lastly, there is another closely related question we did not address. Are historical models good enough to rate crop revenue insurance when there is no futures and options market? This deserves more research given the demand for revenue insurance in those markets is obvious since a functioning price risk market often does not exist.