implied probability distribution

Discussion in 'Trading' started by Lobster, Dec 31, 2002.

  1. I was just thinking. Let's say a (liquid) stock is trading at $100 per share. That means that the average opinion right now is that the stock should be worth $100. But you don't know anything else about people's opinions. It could be that 50% think it should be trading at $90 and only 10% think it's worth $110. Or the other way round. You can get an indication of these figures by looking at how the stock spikes, especially intra-day, or you could try to poll people.

    Has anyone done research in this field?

    How can you get accurate data as to what side would be the surprise side and by how much?

    How can you apply such data?
  2. Options give a good clue, but is that really it? Can't you do something with just price and volume of the underlying?
  3. Lobster,

    Actually, the market price is more like a median value than an average of the distribution. If the stock is at $100 and one the shareholders changes their opinion of the price from $110 to $120, the market price will remain unchanged. If one takes the cumulative shares of price opinions (ranked from highest to lowest) and cut it at the float, one gets the market price. That large numbers of non-owners assign a low value to the stock is irrelevant and that some owners assign a high value to the stock is irrelevant to the instantaneous market price. Its the shifting opinions of the people nearest the market price that make the difference and define the price. (OK its a bit more complicated than that if there are shortsellers, but you get the idea)

    The other tricky aspect is that the market price (and OHLC values) impacts each participant's opinion of price. If the price starts at $100, and I think its only worth $90, but then the price pops to $105, then I might revise my opinion upward on the uptrend (or revise it downward if I think that the price pop is the exhaustion of a rally).

    Interesting problem, though. I think that the price of options provides the most information. One could look at Level II data, but that is notoriously unreliable as people try to game the system with phony outside bid and ask volume. Maybe Volume by Price could shed some light on the distribution?

    Happy New Year,
  4. Actually, this topic was brought up in the last Market Wizards book by an individual who had made a small fortune in a short period of time betting against the implied wisdom of the marketplace at certain times...

    Basically, I think the question and solution has to be applied to each market individually, as opposed to making this a one size fits all problem...Certain markets have different volatility profiles, skews, etc...and also will trade differently in advance of earnings, expirations, etc...Also, if applied to one equity, as opposed to an entire basket of equities(i.e. OEX, SPX) you have different considerations...

    Just from my own standpoint, I have always felt that the many individuals who have been interviewed and asked this question have always said that the B-S does not actually work as anticipated and therefore they always had the edge in the surprise side of the trade...After all, with individual equities, its kind of like the bookie making the market, he/she needs enough interest on both sides of the market to make the trade, but he/she is not dealing with the probabilities of "price shocks" and therefore the smart money or informed money is going to see something that they want and maybe temporarily affect the balance...
  5. I view the bid/ask sides as giant mountains. As you get deeper into the ask side, more and more people are willing to sell at that price. Likewise, as you get deeper into the bid side, more and more people are likely to buy at the cheaper prices.

    That small valley between these two mountains is the spread. It is where bidders are just barely willing to buy something from someone just barely willing to sell it.

    However, if something extraordinary occurs (news, numbers, etc), then one mountain could suddenly shift, kind of like an avalanche. Suddenly, if the news is horrible, the ask mountain will jump towards the bid mountain. Or, the bid mountain will jump away from the ask mountain. This causes problems in the valley, where specialists live to screw everyone who ventures into the valley.