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.
SEEKING BREAKEVEN
“Predicted price spreads” shows the upper and lower breakeven prices computed by the LLP option model for corn, wheat, oats, soybean meal and soybean oil. These are prices of the underlying December futures contracts at expiration that will generate zero profit or loss from a delta-neutral trade — that is, hedging the purchase or sale of calls by the ratio of 1.00/delta while taking the opposite position in the underlying futures contract.
As shown in “Building a better strangle” (Futures, March 2009), the market’s expectation of the probable price spread at expiration determines the slope, or delta, of the call price curve at every strike price. While the strangle suggested the sale of a call at the upper breakeven and a put at the lower breakeven, an alternative trade that sold a ratio of 1.00/delta calls at the current strike price was outlined in “Profiting in trendless markets” (Futures, June 2009), as a delta-neutral trade that included hedging the sale of calls by a long position in the futures contract.
The delta-neutral trade suggested in June 2009 used $4.30 and $5.20 strike prices for calls on September corn futures when September corn was priced at $4.225 per bu. The downside breakeven futures price was approximately $3.50, which means that the current September futures price of $3.27-6 on Aug. 14 would result in a loss. However, protection might have been obtained by the purchase of a call at the upper breakeven price and a put at the lower breakeven. Either would have been less expensive due to the distance from the futures market price.
As a result of the protective put option, on Aug. 14 a $3.40 put on September corn was priced at $1,087, which at this time would offset the loss produced by a declining $4.30 or $5.20 futures contract. A continued decline in the futures price at the September expiration might be expected to carry with it a corresponding gain in the put value.
At breakeven, the option price should increase at the same rate as the underlying futures. “Sept. ‘09 corn put options” shows that on Aug. 14, just seven days before expiration, the put price curve has moved close to the intrinsic value (strike - futures price) so that for strikes of $3.35 and above, the put price is changing at approximately the same rate as the underlying futures. Thus, the $3.40 put would provide complete protection if corn futures continued to decline.
Protection from increasing call prices on the upside of the delta-neutral trade would be provided by the initial purchase of one call at or near the upper breakeven price. Increases in the futures price should offset one of the short calls, while the protective call should rise at the same rate as the futures contract once the breakeven level is reached, equaling the delta of 1.00 attained by the second short call.
“Delta-neutral trade” describes an example trade selling two $3.40 calls on December corn when the futures price is $3.2775 on Aug. 14, 2009. Although the computed delta value is 0.477, we will use a rounded ratio of two calls to one futures. Some protection at the upper and lower breakeven prices, where the option price is expected to change at approximately the same rate as the future, is provided by a call at the $3.90 strike and a put at a strike of $2.90. The protective put and call are expected to eliminate much of the gamma risk, which is the rapid increase in delta values with the approach of expiration.
The example trade should be viewed as experimental, with actual results measured with more accuracy from Aug. 14 through the expiration of December options and futures.
FUTURE SPREADS
“Predicted price spreads” summarized the market’s view of potential high and low prices at expiration. In addition to the upper and lower breakeven prices, the exhibit shows the high and low prices over the past 100 days. Market volatilities are generally measured by past price changes that are assumed to be reflected in future variations.
For most of the futures and strike price pairs on “Predicted price spreads,” breakeven price ranges are close to the 100-day price range. Corn, wheat and oats show breakeven price ranges that are lower than the past 100 days, especially in the case of wheat, where the market is not giving much credence to the high end. The wheat breakeven range is more descriptive of the actual price range in July and August, approximately $5-$5.75.
As shown by the option models, charts and tables presented here, a trader must make decisions in a price world that has boundaries. Computed option price curves show that predicted and actual market prices are almost equal, meaning that trading decisions take place in a narrow range. It is an advantage to know how prices are formed and the mathematical foundations that create the option market.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.
