How Likely Is Oil to Hit $100 a Barrel in December, 2007?

An article from Bloomberg caught my eye yesterday: $100 Oil Price May Be Months Away, Say CIBC, Goldman. Saying that oil could hit $100 a barrel is easy enough to say. Talk is cheap. But are people willing to put their money where their mouths are? Is anyone betting that, in fact, oil will be at this level in December? What kind of odds are the market giving for this to happen.

As we shall see, the market is suggesting that is very unlikely that the price of oil will hit these levels.

The Future Price of Oil

An oil future, is a "contract to buy or sell certain certain goods, such as oil, at set prices at a predetermined time in the future". These are available for purchase at Nymex.com. At the time of writing this a future contract for a barrel of light sweet crude delivered in December 2007 is selling for $74.77. Even taking into account the time value of money this is nowhere near $100.00.

What the future price does not tell us though is how likely the price in December 2007 is likely to vary from $74.77 (both higher and lower). To take that into account, we need to examine option prices.

Call Option Prices for Oil

The Glossary of Economics Terms defines a call option as "a contract that gives the bearer the right to buy a share at a given price". In terms of oil prices, a call option gives the bearer the right (which he can choose not to exercise) to purchase oil at a specified price for a specified delivery date. The right to sell at a given price is known as a put option.

The price for a European-style call option (the difference between American and European style options is explained here) for December 2007 delivery at $100 a barrel is selling for 23 cents.

That means if the price of oil winds up under $100 in December 23, then the option is worthless. If oil winds up above $100, then the option is worth the difference between the price of oil and $100. So if the price of oil goes to $120, then the option is worth $20 - an option you paid only 23 cents for.

Given that the price of the price of the call option is a mere 23 cents, it does not appear that the market believes oil prices will reach $100 in December 2007. However, we can estimate how likely the market thinks is to happen by using an option pricing formula.

Black Scholes Option Pricing Formula

Here is where the analysis gets a bit complicated, but I will leave out most of the math. The Glossary of Economics Terms explains how the Black Scholes equation works:

The Black-Scholes equation is an equation for option securities prices on the basis of an assumed stochastic process for stock prices.

The Black-Scholes algorithm can produce an estimate the value of a call on a stock, using as input:

- an estimate of the risk-free interest rate now and in the near future
- current price of the stock
- exercise price of the option (strike price)
- expiration date of the option
- an estimate of the volatility of the stock's price

From the Black-Scholes equation one can derive the price of an option.

If we assume the risk free rate is about 4%, we have all of that information except the estimate of volatility of the stock's price. However, since we have both the current price (74.77) and the strike price (100.00) and the price of the option (0.23) we can determine the market's estimation of the volatility of the stock's price. The market's estimation of volatility is known as implied volatility.

You can calculate the implied volatility directly using the equation, but the equation is rather complicated and I want to make this as simple as possible. Instead it is much easier to determine the implied volatility by trial and error by using a Black Scholes calculator. It would appear that given our prices, the implied volatility is somewhere around 29% a year. Note that the implied volatility you get will be slightly different if you use a strike price which is closer to the future price - a phenomenon known as volatility smile.

Interpreting Implied Volatility

Implied Volatility is a measure of the standard deviation in expected price exactly one year from today. We calculated the standard deviation at 29%. Thus the range of prices at the 95% confidence interval (which is 2 standard deviations) is +/- 58% (29% x 2).

However, we're interested in the range of prices in 4 months time. The calculation for that standard deviation is the root of the length of time (in years), times the standard deviation above. Since we have 1/3 years, the standard deviation for the 4 month period is sqrt(1/3)*29% = 16.7%.

We can expect then, with 68% certainty (one standard deviation), that the price of oil in December 2006 will be 16.7% higher or lower than $74.88; a range spanning $64.23 to $87.29. We can expect with 95% certainty that oil prices will be 33.4% higher or lower than $74.88; a range spanning $56.18 to $99.80. Using our figures $100.00 is 2.015 standard deviations from $74.77, implying the implied probability that prices will reach $100.00 or higher is 2.19%

Conclusion - Oil Prices Unlikely to Hit $100 in December

Although talking heads in the media may frighten us with stories of $100 barrels of oil, the people who put their money where their mouths are do not believe this will happen. It might happen - the market is suggesting it has around a 2% chance of occuring. But it would appear to be quite unlikely.

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