Estimating Return Probabilities from Option Prices

Summary

The document asks whether option implied volatility can reveal the probability that a stock will exceed a specified return threshold by a given expiry. It frames the question with an at-the-money option example and asks whether out-of-the-money options or combinations of options could estimate a one-sided probability.

The response points to research on extracting implied probability distributions from option prices and the underlying, alongside a software example and an introductory article. It provides references rather than explaining a particular estimation procedure or presenting empirical evidence. The implied volatility of a single at-the-money option is not itself developed into a probability calculation here; the reader would need to consult the cited methods and account for their assumptions and limitations.

Key ideas

• Option implied volatility raises the question of whether a one-sided return probability can be inferred.
• A single at-the-money implied volatility does not provide a calculation method in this document.
• Option prices can be used in methods that estimate an implied probability distribution.
• The response directs readers to research and examples but does not compare or validate them.

Tags

# Is it possible to calculate implied probability of >=X% return based on implied volatilities from options


# Is it possible to calculate implied probability of >=X% return based on implied volatilities from options












My question is: Is it possible to imply either the upside or downside (one sided) probability from looking at implied volatilities of stock options?

Let's take an example: say you had Stock A at $50, with a 3M ATM Option with an Imp. Vol of 20%.

Is there a way, using perhaps non-ATM options, or some combination of options perhaps(?), to calculate the implied probability of Stock A being >10% by expiry (let's say 3m)?

## Answer by Flux (score 1)

https://quant.stackexchange.com/a/53179

You can find a variety of methods in this paper: Mizrach, Bruce, Estimating Implied Probabilities From Option Prices and the Underlying, in Cheng-few Lee and Alice C. Lee (eds.), Handbook of Quantitative Finance and Risk Management, New York: Springer-Verlag, 2010, 515-29.

MathWorks has an example of a method coded in Matlab: Estimating Option-Implied Probability Distributions for Asset Pricing.

You may also be interested in this simpler article: Option Prices Imply A Probability Distribution

To find other methods, you may need to search for papers on Google Scholar.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.