1
$\begingroup$

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)?

$\endgroup$
2
  • 1
    $\begingroup$ You can get the risk neutral implied probability by pricing an undiscounted digital call or put - the distribution is only valid on expiration date. The pricing is based on the digital price with skew - for a digital put: $P=N(-d_2)+\frac{d \sigma}{dK}\frac{\partial C}{\partial \sigma}$ where $C$ is the price of a vanilla call - i.e. black scholes digital put + skew*vega. $\endgroup$ May 22, 2017 at 19:04
  • $\begingroup$ Right. More generally, the full risk-neutral distribution can be inferred using the so-called Breeden-Litzenberger identity. $\endgroup$
    – Quantuple
    May 23, 2017 at 8:29

1 Answer 1

1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.