A note on agricultural options and the variance of futures prices

Abstract

he recent introduction of options on agricultural futures has fueled a growing T research interest on issues ranging from risk-return characteristics of option hedging strategies to the valuation of commodity options. Valuation models for options on common stocks have been extensively used ever since Black and Scholes published their seminal paper in 1972. However, direct application of the traditional option pricing models in evaluating agricultural futures options may not be appropriate, especially if the assumptions used to derive the model are not met. The objective of this article is to draw attention to the validity of the assumption of constant variance of the underlying futures price within the framework of an options pricing model. Furthermore, we aim to improve on current aproaches in this area by utilizing recent evidence in futures markets.Recent evidence which appeared in this Journal (Castelino and Francis, 1982;Anderson, 1985;and Milonas, 1986a) and elsewhere (Castelino, 1981 andMilonas, 1986b) strongly supports Samuelson's (1965) maturity effect hypothesis (futures variance increases as maturity nears) for a wide range of agricultural, metals and financial futures contracts. The agreement of the above studies on the maturity effect is due to the use of a large number of observations and to an improved methodology over previous methodologies which presented mixed results (Miller, 1979 andRutledge, 1976). The new methodology attempted either to control for nonstationarity sources such as the "year effect", "month effect" or "contract month effect" (Castelino, 1981and Milonas, 1986a, 1986b; or to explicitly capture the seasonal factors (Anderson, 1985). Direct measurement of the above nonstationarities was given by Milonas and Vora (1985), whose study also suggested that the incorporation of the above nonstationarities in methodologies dealing with futures prices is required in order to avoid serious biases.Hauser and Neff (1985), use agricultural options as an example in which direct

The effects of USDA crop announcements on commodity prices

“…Anderson (1985); and Milonas and Vora (1985), found that price volatilities of agricultural commodity prices are nonstationary. First, there is a month effect.…”

“…Such a monotonic effect will bias the results unless proper measures are taken. Milonas and Vora (1985) presented evidence that futures prices in agricultural commodities, maturing in different months behave differently. An old crop contract is expected to exhibit higher variability than a new crop contract.…”