Prices of December futures for corn, wheat and oats reached the peak of a four-month rising trend in early June 2009. What followed was a difficult summer for all grains, including the bean complex — soybeans, meal and oil. Causes for price declines included a combination of increased planting, good weather conditions and lower demand for grains. The option market cannot predict what will happen to grain futures prices, but it can and does predict the likely range in futures prices over the time to expiration.
“Calls on soybean futures” shows the LLP options model’s analysis of calls on November 2009 bean futures. Using 15 strike prices on Aug. 14, the model computes call prices predicted by a regression equation. Also shown are the delta (slope) values and the upper and lower breakeven prices for delta-neutral trades at each strike. A measure of relative price volatility is the 6.78% premium of predicted call price over the strike at the current futures price. This is the “time premium” that decreases with the approach of expiration.
Option price curves for calls on December 2009 corn, wheat and oats are combined on “Grain call options”. The three curves illustrate the market’s assessment of their relative volatility. Although the distances between them are small, there is evidence that their volatilities go in order of corn, oats and wheat. The ranking of volatilities is supported by the time premiums on the table (see “Vol compared”). Soybean meal and oil are included as adjuncts to the grain collection. Option price curve time premiums show that corn calls are the most volatile, while bean oil is the least volatile.
In addition to the time premiums for the December calls, the Black-Scholes model is used to generate standard deviations of expected underlying asset returns to measure the B-S volatility measures for grains. Because Black-Scholes adjusts for the time to expiration (from Aug. 14, there are 70 days for the soybean November calls and 98 days for December calls), November soybean calls are included in the list. The same volatility ranking occurs in LLP time premiums and Black-Scholes standard deviations.
Microsoft Excel worksheets for call and put options, and for Black-Scholes theoretical option values, are available for download as free tools at futuresmag.com.