Yesterday (Tuesday), the DOE released its latest Short Term Energy Outlook (STEO) to mixed reactions.

Prices rose in the hour after the release, but the recovery did not have any legs and the markets stagnated to close.

Understandably, this month’s STEO has few surprises: The settle price for the Nymex WTI contract for April delivery was revised $1 higher to $79.00, but May remains the same at $80. Prices are expected to average above $80 per barrel this spring, rising to an average of about $82 per barrel by the end of the year and to $85 per barrel by the end of 2011.

For those looking to trade the short-term market, the EIA did include one new, very interesting feature: the probability of prices exceeding certain levels, as seen in the graph in today’s issue of The Schork Report.

The calculation is actually a Cumulative Density Function (CDF), a component of the Black Scholes option pricing formula and similar to the confidence intervals the DOE and The Schork Report has been publishing in recent months. The DOE’s calculations put an 11.54% probability that crude oil prices will be greater than $100 by August, and a 19.90% probability that prices will cross $90.00 by May.

Interested readers can download the spreadsheets from the EIA’s Web site and try their own values, but the calculation is more interesting when used in the context of purchasing options.

Goldman Sachs recently expressed enthusiasm for “significant hedging opportunities” in options against upside risks, i.e., buying options could pay out big if prices start shooting higher, and those options are currently cheap because option pricing implies oil is more likely to fall than it is to rise. This is counter to the $95 oil that Wall Streeters, chief amongst them Goldman Sachs, are predicting. So is Goldman placing more emphasis on fundamental factors than statistical i.e. being subjective instead of objective?

Let’s keep things simple, consider the payout of an option like the payout on a horse race. As of Monday’s $82.31 close for May WTI, a $75 put option (the price of betting on a horse named Fundamental) was priced at $0.88. According to the DOE’s CDF for WTI, the probability of Fundamental crossing the $75 finish line is 18.9%, which makes odds of 9:2.

If Fundamental runs 11 races, you expect her to lose 9 times, but win twice. In other words, you will pay a total of $9.68 to play all 11 races, i.e. you are going to walk home empty handed 9 times, but pocket $7.31 twice. That comes out to an average win of $0.45 a race.

However, there is another horse on the card for that day’s race. Bookies are fixing odds on this horse, Double Dip (which was sired by Bubble 08) at 5: 1 (probability of 16.67%) that she will cross the $90 finish line. Double Dip was priced at $0.69 Monday night. Therefore, if Double Dip runs 6 races, we would pay $0.69 each time for the chance to win $7.69.

In the end, we would pay a total of $4.14 on the expectation that our horse would come in (figuratively and literally) once for an average expected payout of $0.59 a race.

Why would a bookie make the payout on Double Dip more attractive than Fundamental? Because the bookie figures the chances of Fundamental crossing $75 are better than Double Dip crossing $90. Therefore, Goldman… uh… we mean… the “bookie” will fix the odds so as to attract more money to bet on Double Dip.

Of course, options pricing is more complicated than simple odds. The models used by options writers factor out volatility smiles and tweaked versions of the normal distribution.

Meanwhile, contrary to popular opinion (outside the canyons of Wall Street that is), fundamentals do eventually apply… and the mathematics cannot always capture this. Regardless, it seems odd for speculators to be so narrowly bullish when the math sits on the other side of the fence.

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*Stephen Schork is the Editor of The Schork Reportand has more than 17 years experience in physical commodity and derivatives trading, risk systems modeling and structured commodity finance.*