Econbrowser

Superb post. As a futures professional, wanted to note that your series of articles wrt oil and the trading thereof, have been good reads.

Query/request - an article about futures price distortion due to "always long" index funds.

I disagree with above. Boone Pickens makes a persuasive argument to the effect that world demand is increasing and (in the near term) there is little prospect that supply can keep up ... AND ... that prospects for "something negative" (crisis in Venezuala, Nigeria, pipeline/refinery damage, etc) are ever so much greater than for "something positive" (a new oll field being brought on line, etc).
Mr Pickens predicts $100/bbl price prior to end of 2006.

How do you get the other numbers for the online Black-Scholes calculator? This is fascinating, but I'm not an economist and want to play around with the calculator.

Thanks.

Even if you assume that Mr. Pickens is correct about the relative probability of positive and negative events influencing the price, that still does not necessarily say anything about what the market price will be at any particular point in time.

It's often not hard to know which way the market is going _in the long run_...but you can still lose plenty of money assuming it'll do something similar in the short run.

I'd rate the odds of it hitting $100 in the next year quite a bit higher than the odds of any kind of substantial fall...but not so high I'd be willing to bet on it being $100 on any particular day.

I am afraid you are confusing risk-neutral measure and physical measure. Probabilities implied by option prices are NOT the consensus probabilities of the market. This may sound a bit technical, but the difference is huge.

For example, consider a stock worth $100 now, and suppose everybody believes that in one year it can only go up $10 (with probability 70%) or down $10 (with probability 30%), and assume that the interest rate is 0. It is easy ot see that the $100 strike call is worth $5: if one buys this call and sells 1/2 share then one gets $5 in one year with no risk. On the other hand, expected payoff on this call is 70%*($110-$100) = $7. Option prices are driven by no-arbitrage conditions, not by expected payoffs.

I agree with mic in the previous comment. The option prices are set by market expectations about volatility and do not reflect the odds of any particular price level.

The market's expectations of future prices are imbedded in the spot price of the asset and not in the options prices.

I don't think I'm confused about this, Mic, but I'm happy to use your comment as an opportunity to try to be a little more clear.

The Black-Scholes formula is derived from the no-arbitrage condition associated with a particular dynamic hedge, and Mic gives a very nice example of why option prices have to satisfy these kinds of conditions. By the nature of the particular dynamic hedge considered by Black-Scholes, all that the condition ends up allowing you to infer is the variance of the distribution. In Mic's example, if instead the price could be up 20 or down 20, the option would be worth 10, not 5. So in Mic's example, you could infer from the option price the spread of the distribution but not the particular probabilities. In my analysis, I was only using the option price to get the variance of the density that I plotted, and was coming up with the mean separately from the futures price itself. It is true that the assumptions you need to make in order to infer the variance from the option price are different from the assumptions you need to make in order to infer the mean from the futures price. To use Black-Scholes, you need to assume a lognormal diffusion, whereas to use the futures price, you need to assume risk neutrality. I was making both sets of assumptions and using both markets in order to make statements about the full probability distribution.

A particular person such as Simmons or Ayer or the intended reader of my post has an opinion about both the mean and the variance, so a particular person would have an opinion about whether buying or selling a particular option at a particular price might or might not be a good deal. Since those opinions were the focus of my post, that is how I chose to organize my presentation.

Here's more on how to use that Black-Scholes calculator, Dan. For "current future price" you put in the price you'd have to pay right now for the underlying futures contract on which you're looking at an option. In my first example, I was looking at an option on the June 2006 futures contract, and the closing price on Tuesday for the June 2006 futures contract was $62.04. For "option strike price" you put in the strike price of the option you're considering, for example, input 80 for the $80 June 2006 call option. For "days to expiration" you enter the number of days between now and the date of expiration of the contract you're looking at. For example, the June 2006 contract expires on May 22, 2006, which is 319 days from now. For "annual interest rate" you want the risk-free rate, which you'd get from a Treasury security at 3.5%. For "price volatility" you put in the value of s quoted in percent, for example, for s = 0.33, you'd enter 33. If you put in those values, you'll get a price for the call option of $2.41, which is what that option in fact sold for on Tuesday's close, confirming that the implied volatility on that option was 33%.

Is there any data on how well options predicted large swings in oil prices?

Coming at this with no experience whatsoever, I would think the long term strategy would be to plot a fairly gradual increase in price, and hedge that position. occasionally, you might be losing money, such as in the big swings, but that on average, swings are predicted more than they materialize, leading the institutional strategies towrds a conservative path that grants that they will lose in the rare big swing scenarios.

Coach, one thing you can do is compare the volatility that's implied by the current option prices with what the volatility of crude oil price changes has been historically. If you look at the standard deviation of changes in the log of crude oil prices going back to 1974, you end up with a historical volatility of 29%, a bit below the 33-36% implied volatility as currently priced in the market. So, the market is a bit more concerned about the possibility of a big move up or down at the moment than you would have been if you drew a month at random over the last quarter century.

The discussion given is confusing, because it suggests that the derivation of the option-implied probabilities depends on the Black-Scholes model. In fact, one can obtain these probabilities directly from the option prices.

For example, suppose that we wish to find the option-implied probability that oil is over $70 in December. If we are long a $69 call, and short a $70 call, we get paid $1 if oil is over $70, and $0 if oil is under $69. (For clarity, let's ignore the case where oil is between $69 and $70.) The (risk-neutral) price of this position in cents is the percentage chance that this position pays off, i.e. that oil is above $70 in December.

The price of this position, as of this writing, is $3.24-2.95, or 29 cents, which gives an option-implied probability of 29%. Note that this is very close to the 30% one gets from the table in the original post.

For further discussion of this point, and the point made by mic above, readers may consult, for example, "The Concepts and Practice of Mathematical Finance", by Mark Joshi, Ch. 6, Sec. 3.

It's worth noting that Joshi restates mic's point in a number of ways. Perhaps the clearest is "we can regard [the option-implied probability] as the probability the market is choosing to price with."

$75-$85 bbl. No higher.

Ever bet those football pools at work?
Amazing how accurate those point spreads are.