The regression equations computed for March 2010 soft futures calls on Dec. 15 provide a method of predicting options prices for any strike price given the underlying futures price. Over time, the accuracy of the predictive price curve declines; therefore it is expected that it is most useful on the same day that the equation is calculated. However, the predictions can be projected over several future days to estimate the impact of changes in the futures price and expectations by the options market.
For example, the call price equation for March 2010 cocoa futures on Dec. 15, 2009, had the following form:
ln(W/E) = -2.8435 + 9.2241(ln(F/E) – 7.9388 (ln(F/E))^2
ln(W/E) = natural log of
(predicted options price/strike price)
ln(F/E) = natural log of
(futures price/strike price)
The closing price of March 2010 cocoa on Dec. 15 was 3365, and the options price equation for cocoa in “Sweet deal” used this futures price as the value F. Strike prices (values of E) ranged from 4100 to 3200 in steps of 100 ticks.
After the natural log of W/E is calculated, the ratio of the predicted call price-to-strike price for each strike price is equal to the following antilog.
W/E = (2.718281)^ln(W/E)
The predicted call price is
W = E x W/E
A short-range example of the predictive price curve uses two other days’ closing futures prices (Dec. 18, 2009, and Jan. 4, 2010), with the market prices for call options calculated on the original set of 10 strike prices.
On Dec. 15, the prices generated by the regression equation have both plus and minus variations from the actual market prices, while on Dec. 18 (using the initial equation as a benchmark) all of the market prices were slightly lower than the predicted prices, and on Jan. 4 significantly lower.
As shown in “Volatility juices options premium,” the distance between the Dec. 15 and Dec. 18 price curves is relatively narrow, while the Jan. 4 difference escalates from the higher strike prices to the lower strikes (and highest option prices). The implication is that between Dec. 15 and Jan. 4, the call options curve for March 2010 cocoa rotated so that the slope at the upper right of the option price curve fell, while the lower end
“Finding an edge” shows the options price curves on Dec. 15 and Jan. 4. Changes in the shape and height of the option price curve reflect two possible explanations in combination: (1) market recognition of the approaching expiration date in March 2010, and (2) market consensus regarding a lower price for cocoa futures over the following months.
The first explanation – that the rotation is caused by the shortening of time to expiration – is supported by the lower heights of the five price curves between Dec. 15 and Jan. 4, as shown on “Volatilities compared.”
The second explanation is supported by changes in the upper and lower breakeven futures prices at expiration (futures prices in March which would result in zero profit or loss on a delta-neutral trade between March cocoa futures and call options on March futures). Between Dec. 15 and Jan. 4, the upper breakeven price for the 3300 strike price fell from 3785 to 3624, while the lower breakeven price gained from 2986 to 3010. The value of one tick in cocoa futures is $10.
Price curves for futures options generally show small deviations from expected prices according to regression analysis, indicating that the market expectations for upper and lower delta-neutral breakeven prices at expiration are the basis for the slope at every strike price and thus the call or put price at each strike price. Volatility differences among underlying futures contracts are directly involved in options pricing in measurable quantities.
Soft futures options may provide examples of the need for a different view of volatility. That is — as shown by the charts and tables previously described — volatilities are primarily associated with short-term price variations. It would be easy for volatility measured by day-to-day or week-to-week price variations to miss larger trend movements in price, and therefore understate the breakeven price spreads that are the foundation of options market prices.
Indeed, predictions of upper and lower breakeven prices several months before expiration are often exceeded by market prices. It may be that, rather than being expected price boundaries, upper and lower breakeven prices are targets that the market tends to match or exceed.
Despite the feeling that target prices are being established, “March breakeven prices” presents those that are calculated on Jan. 4, 2010. By the March expiration date, it should be obvious whether the futures price movements will stay within their consensus boundaries, or use the breakeven prices for target practice.
Soft futures are diverse in terms of the commodities they represent, but they have similar characteristics in options valuation and trading. The similarities disclosed by paired volatilities and options pricing may produce valuable spread trade possibilities.
Paul Cretien is an investment analyst and financial case writer. His e-mail is