What Option Prices Reveal About Future Price Distributions and Paths

# Is it possible to use a series of option prices to predict the most likely path of an asset?


# Is it possible to use a series of option prices to predict the most likely path of an asset?












I've always wondered about this.

If you have a series of options, with the expires spaced let's say one week between them, and you search for each expiration date the option with the smallest premium, would the series of strikes represent the current market predicted path of the asset?

Can you use that information to speculate the spot price?

I believe that this paper is about a similar approach: http://ideas.repec.org/p/ihs/ihsesp/104.html

## Answer by glyphard (score 9, accepted)

https://quant.stackexchange.com/a/242

If you think of a path as a series of ranges then your idea kind of makes sense. However, I don't think you would get a path out of this approach, just a series of ranges.

Example: Taking one expiry, the prices in a chain imply a range of price movements between today and expiration.

Take the SPX(at say 1300) and VIX, for example, is at 15.8 and the SPX option chain that you are looking at is 30 days from expiry. That tells you that there is approximately a 68% probability that the SPX will be between approximately 1370 and 1230 at the end of 30 days, or a 68% probability that it will be within 1% of 1300 in 1 day.

Running this example on multiple chains would only expand the range(implied vol is increasing in later expiries), or contract the range(implied vol is decreasing in later expiries).

----- idea ----- If you had access to a standardized/liquid market of path dependant options, you might be able to narraw the range down somewhat.

If you did arrive at a narrow path estimate, it would change frequently with volatility... what would be the value of this path estimate?

## Answer by egoroff (score 10)

https://quant.stackexchange.com/a/272

A further comment on user214's answer : the probability distribution of the future value of the index that you imply from option prices is its distribution under the (market) risk-neutral measure, which generally different from the true historical measure. In particular, option prices do not give information about the risk premium. There is a vast literature about this, but a good start is this paper from Chris Rogers and Steve Satchell.

Furthermore, European option prices give you information about the marginal distributions of the index at fixed maturities, but they give you no clue about the dynamical properties of the value process, that is, the distribution of the paths.

## Answer by onlyvix.blogspot.com (score 6)

https://quant.stackexchange.com/a/245

Just would like to expand on user214's answer: you can use options to predict underlying in probabilistic sense. As you know option prices imply a certain distribution - you can find expected value for stock, and volatility around that value.

If you assume a particular distribution (for example normal distribution for returns) you can derive expected high (over some period of time), expected low, expected range, expected drawdown, probabilities for different paths, etc. That is not something you should do in practice, or do it and know the limitations of such model-based estimates (that is what I do in trading).

If you have access to exotic, particularly path-dependent options you can fit more complicated models, and figure out what they predict about the stock price. While you can fit more realistic models to only vanilla options, such fits are not robust, because they depend only on terminal distribution of the underlying, and not its path.

## Answer by vonjd (score 5)

https://quant.stackexchange.com/a/273

This is the paper for you: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1107464

From the abstract:

> The shape of the volatility smirk has significant cross-sectional predictive power for future equity returns. Stocks exhibiting the steepest smirks in their traded options underperform stocks with the least pronounced volatility smirks in their options by around 10.9% per year on a risk-adjusted basis. This predictability persists for at least six months, and firms with the steepest volatility smirks are those experiencing the worst earnings shocks in the following quarter. The results are consistent with the notion that informed traders with negative news prefer to trade out-of-the-money put options, and that the equity market is slow in incorporating the information embedded in volatility smirks.

For information on the volatility smirk a good starting point is here: http://en.wikipedia.org/wiki/Volatility_smile

## Answer by Richard Herron (score 3)

https://quant.stackexchange.com/a/244

If you're asking "can I get a prediction of a future price from an option chain", then, no, I don't think so. The value of an option does not depend on the underlying stock's drift, or price expectation, because this expectation is already reflected in the stock's current price. Given the risk-free rate and the time to expiration, all that you can back out of the option price is the implied volatility.

The intuition is that we don't really value options in absolute terms, but in terms of the underlying stock.

## Answer by userid is i (score 2)

https://quant.stackexchange.com/a/37978

I think option prices are related to future stock prices. First, VIX moves against stock price movement, and VIX is computed with a volatility number that comes from current stock and option prices. Second, while the B-S formula comes from hedging strategy and does not depend on the drift parameter in the stock model. options may also be used for speculation or investment, so standard "efficient market" reasoning is relevant for pricing, in particular their expected value should not be far from 0 short term. Then a range of option prices can be used to fit a probability distribution. Some links that purport to do predictions: https://www.investopedia.com/articles/optioninvestor/03/091003.asp www.optionvox.com https://www.barrons.com/articles/SB122514292217673547