In mid-December 2011, the Organization of Petroleum Exporting Countries (OPEC) surprised the energy markets by deciding to increase oil production with a new output target of 30 million barrels a day. Bloomberg reported that crude oil for January declined $5.19, or 5.2%. On Dec. 14, March crude oil fell $5.11 to $95.37 — up from $76.53 on Sept. 4, but at the time on a short-term downtrend.
“March 2012 calls” (below) shows four energy futures: Crude oil, heating oil, natural gas and gasoline, along with March calls on Valero Energy Corp. On this chart, option prices and underlying futures and stock prices are standardized by dividing by the strike price. The comparison indicates that the equity options of Valero are significantly more valuable in terms of future price volatility than options on the four energy futures. Crude oil and gasoline calls are bounded by the more volatile (in the option sense of the word) natural gas and the less volatile heating oil contracts.
Valero also is more valuable in terms of option pricing when compared with several energy equities (BP, Exxon Mobil and Chevron). The chart “Calls on energy equities” (below) again places Valero considerably higher than the other three call price curves as standardized by dividing the underlying stock and option prices by the strike price. The larger expected future price variability of Valero may be a function of its product mix, which includes ethanol and heating oil, or simply traders’ assessment of future stock price trends.
A more complete comparison of option market forecasts for energy stocks futures is shown on “Delta hedge forecasts” (below). Heights of the call option price curves are measured at the point where the underlying futures or stock price is equal to the strike price. The height of an option price curve is determined by two prices for the underlying at expiration that will permit a hedged trade between futures or stock and corresponding options to break even, with neither profit nor loss. These are the upper and lower breakeven prices of a delta trade, in which delta is the slope of the option price curve — showing the price change for the option versus a change in the underlying price.
“Delta hedge forecasts” shows that Valero Energy has the highest option price curves and largest expiration breakeven price spread for January 2013 and March 2012. The options market does not pick a direction, thus the upper and lower expiration prices equally are likely. It is possible that either one or both prices will be achieved in the equities market well before the expiration date.
Of the four energy futures’ — crude oil, heating oil, gasoline and natural gas — March contract, the most correlated with the Valero Energy stock price is heating oil.
“Valero & heating oil” (below) contains the daily cumulative percent price changes for Valero stock and March heating oil futures from Sept. 1 through Dec. 16, 2011.
Based on the previous charts and numerical table we expect Valero stock to be more volatile than heating oil futures, and this chart illustrates the difference between the two. Although the directions of price changes are similar, the price movements are larger for Valero, extending from slightly more than plus and minus 20% vs. plus and minus 10% for March heating oil futures.
By using the cumulative price change for heating oil as a guide, it may be possible to improve trades on Valero common stock. A similar trade could be based on variations in the cumulative percent price changes for March heating oil futures where the oscillation is around zero in the absence of a sustained uptrend or downtrend in the futures price.
Cumulative percent price changes for Valero stock and heating oil futures eliminates a problem in terms of differential price movements. Valero stock changes on the basis of dollars per share, with one option point equal to $1. One futures or option point for heating oil is $42,000 (42,000 gallons or 1,000 barrels of heating oil), with the minimum price change 0.0001 of one point, or $4.20.
From Oct. 3 to Oct. 12, 2011, Valero stock gained $4.24 per share, while the March heating oil futures contract increased by 0.1805 points or $7,581. With turnabout being fair play, it would be just as well to use the Valero stock price movements as key to trades in heating oil futures.
Building an option price
Starting with an estimate of a spread in prices for the underlying futures or stock price at or near expiration, one point on an option price curve may be constructed. Fortunately, this is the most important point — the price on the curve that is directly over the strike price, and one at which the delta, or slope, value is slightly larger than 0.50 so that a hedge trade would be approximately two call options held long against one underlying asset sold short.
The necessary ingredients for building the option price are the current futures or stock price, a strike price and upper and lower expected prices at expiration. Several straight lines are used, beginning with a horizontal line called the X-axis. One point on the X-axis is the strike price. For example, March 2012 gasoline futures on Dec. 13, 2011, were priced at $2.651 and a strike price near the underlying price at $2.700.
From the strike price at $2.700 (Point S) a line is drawn up to the right at a 45-degree angle. This is the intrinsic value line on which each point is equal to the underlying price less the strike price. On Dec. 13, the options market forecasts a price range for March 2012 gasoline at expiration from $2.988 (Point U) to $2.407 (Point L) marked on the X-axis on the right and left of the strike price, Point S. The distance SU, $0.298, is drawn as a perpendicular line from Point U to the intrinsic value line at Point B.
The total spread between the forecast breakeven prices is $2.988 – $2.407, or $0.581, equal to the distance LU. A line drawn between Points L and B must rise by $0.298 over the distance $0.581, a slope equal to 0.513. This will be the approximate slope along the option price curve at Point P directly over the $2.700 strike. The height of the option price curve at Point P is equal to the distance LS, ($2.700 – $2.407) x 0.513, which is $0.150.
As a percentage of the strike price, the height of the option price curve is 5.5%, matching the height shown for the gasoline calls on “Delta hedge forecasts.”
Reversing the price estimate technique permits finding the market’s expiration breakeven price forecast when the only data are the underlying price and the market price of a call option where the strike price is close to the underlying.
For example, March 2012 natural gas call prices include a strike price of $3.30 when the futures price is $3.307. By using the 0.50 slope, the lower breakeven price estimate would equal $3.30 less two times the option’s market price ($3.30 – (2 x $0.25) = $2.80). The upper breakeven is estimated at $3.30 + $0.50 or $3.80. These estimates compare with upper and lower delta hedge prices for March 2012 equal to $2.94 to $4.09.
Because many of the variables in the options pricing process are in continuous motion, the correct price at any time is a moving target, but chains of prices move at a moderate pace. Relationships between underlying assets, strike prices and prices predicted by regression or theoretical pricing models generally are stable and manageable.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.