How do I calculate probability distribution of stock prices given option prices?

Question

I'd like to calculate a probability distribution for prices given the option prices for that stock? Any ideas how to do this?

My desire is to do this daily and then see how the price PD changes over time and see if that can give any insight to the market's evolving view. I couldn't find any prior art on the later, any suggestions would be appreciated.

Did you make any progress with this? How did you eventually achieve this? — Homunculus Reticulli, Feb 22 '23 at 23:09

score 7 · Answer 1 · answered Mar 20 '14 at 04:14

7

One approach is to take the entire option chain, and calculate the prices for adjacent butterflies along the chain. The risk / reward of each of the butterflies represent the empirical probability that the market is pricing for the underlying to move between the strikes of the butterfly.

To make sure it is a proper probability distribution, you will want to normalize these empirical probabilities so that the sum of the entire probabilities from all the butterflies equals 1.

answered Mar 20 '14 at 04:14

delta hedge

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Brilliant answer, as it does not rely on any model (like Black Scoles), this method should reflect the true market implied probability. – Bigjim Jun 12 '17 at 13:25
How do you deal with large bid-ask spreads? Would it be better to move the options further apart? – trinalbadger587 Mar 25 '21 at 17:55
@deltahedge You wrote "One approach is to take the entire option chain, and calculate the prices for adjacent butterflies along the chain. The risk / reward of each of the butterflies represent the empirical probability that the market is pricing for the underlying to move between the strikes of the butterfly."
I'm intrigued. Is there a link where I can read more about this?
– Homunculus Reticulli Feb 22 '23 at 23:05

score 7 · Accepted Answer · edited Apr 13 '17 at 12:46

you should have a look at implied probability densities. They do exactly what you are asking - extracting the pricing density from option prices.

This is done by differentiating the option price with respect to the call.

Here are two links. The first one explains the procedure the second one deals with where such densities can be applied

How do I calculate probability distribution of stock prices given option prices?

2 Answers2