Market prices of futures and equity options lie on price curves that are described by log-log parabolas. This means that there is little difference between the market price of an option and the price that is predicted by a regression equation. In addition, each option price is determined by its upper and lower break-even prices — the market’s forecast of the underlying futures or stock price at the option’s expiration date that will produce a zero gain or loss from a current trade that balances the price changes of an option and its underlying asset.
Option prices represent tangent points along the price curve. A line that extends from a point on the horizontal axis (at the upper break-even price) to the intrinsic value line (where the intersection lies directly above the lower break-even price on the horizontal axis) will pass through the tangent point. Thus, an option price curve is shaped by an infinite number of paired upper and lower break-even prices, with each pair generating an option price on the curve.
An option price curve starts with the prices listed by actual market trading, but artificial prices can be added once the regression equation is computed. The large number of strike prices listed and traded for many futures contracts results in option price curves that are smooth, with prices that rarely deviate from the predicted values by more than a few option points.
There is both good news and bad news resulting from such organized and predictable valuation of options. The bad news — that we are dealing with logarithmic calculations — certainly is overcome by the good news of more complete understanding of options and their valuations and the possibility of trading on the knowledge of upper and lower break-even prices.
"Calls on crude oil futures" (below) shows options on September 2011 crude oil futures on June 14, 2011. With the underlying at $100.40, the option price curve increases as strike prices are reduced. Each option price is determined by the upper and lower break-even prices that the market uses to define the price curve. As the strike price increases relative to the underlying, the lower break-even increases more slowly than the upper break-even price because the intrinsic value line slopes down in the same direction.
The delta value, or slope, at the point on the option price curve where the underlying equals the strike price, is approximately 0.5. This means that two calls could offset the price change of one futures contract — a fundamental requirement of the delta trade. The market is pricing September 2011 crude oil call options, with 64 days to expiration, based on upper and lower delta trade break-even prices of approximately 112 and 92. A call at 112 is listed with a premium of $1,260 while a put at 92 is $2,080 at the close of trading on
June 14, 2011.
The trade possibility — buying a call at or near the upper break-even and buying a put at the lower break-even — depends on the market’s logic and accuracy in establishing the break-even prices. For options to be priced for trading, the market must believe that profitable price variations are possible, and even likely. Thus, the upper and lower break-even prices on which option valuation depends should not be viewed as extreme limits that have low probability of being achieved. Instead, these are prices that the market views as entirely possible within the number of days to expiration.
Recent price volatility plays a large role in determining the range of forward break-even prices, and fundamental influences of supply and demand as well as varying cost structures also are considered by the market. An individual trader may adjust the upper and lower prices in response to variables that go beyond normal market information.
Good as gold
A recent and ongoing example of the potential in break-even prices is shown in "Gold & silver: Always good options" (May 2011). On March 1, 2011, December gold futures at $1,435.80 had break-even prices of $1,639.00 and $1,253.00. December silver, at $34.57, had break-even prices of $43.47 and $27.31. The break-even price spread was almost twice as large for silver because of its greater volatility.
By May 2, 2011, December gold had increased to approximately $1,560 and from that point had dropped back to $1,518 on June 13, 2011. On the other hand, December silver exceeded its upper break-even price by hitting $47.18 on April 25 and $47.56 on April 28 before falling to $34.81 on May 12.
One advantage to the purchase of calls and puts at upper and lower break-even prices is that the result of the worst possible scenario (when none of the breakeven prices result in profitable trades and none is used to reduce cost) is known at the time of the original trade.
A sample of 12 futures contracts on June 10, 2011 is shown on "Puts and calls" (below). Although the contracts are all September expirations, the numbers of days remaining vary from 56 to 111. Time remaining and expected price volatility are factors that determine the height of option price curves, with higher curves indicating the market’s expectation of greater changes in the underlying futures or equity price. Direct comparisons can be made between options having approximately equal times to expiration.
It is logical to think that puts and calls on September lumber futures, with the call price curve high at 8.72% of the strike price and 82 days remaining, should be a better speculation than options on soybean oil, with curve height at 3.87% and 77 days to expiration. The dollar index and euro look rather doubtful — even with greater time remaining — because of the market’s low volatility estimates for these currency futures.
Separate but equal
Regardless of the variations in remaining time and expected volatility, the market is expressing itself through current prices of the sample put and call options. During each moment of the trading day, option prices are being set according to the market’s forecast of futures and equity prices up to and through the expiration dates.
From this point of view, all of the puts and calls indicated by upper and lower break-even prices have an equal chance for success because all have been screened and adjusted by high-speed computerized pricing models that have taken account of all the variables that will determine the final outcome.
Over the period June 14 through July 15, seven of the 12 futures exceeded a break-even price, resulting in the peak gains shown on "Results through July 15" (below). September orange juice followed with a $214.50 gain on July 19.
Thus, break-even prices indicate potential price spreads leading up to option expiration dates — permitting trades involving purchase of calls and puts at strike prices near break-even prices. They also may help in the opposite strategy of selling options by suggesting the separation needed from the current futures or stock price.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.