Hello community, I am curious to know if some of you use probability density functions to analyze the market sentiment. An example of those is attached to this post. Basically, the blue line is the risk-neutral probability distribution for ES futures recovered from options prices expiring on 19 december, and the pink line is the distribution created for the same underlying just with the atm volatility. I think this information might be quite valuable, on the particular jpeg attached we see that todays options prices imply that there is a slightly higher probability for ES to trade at higher levels until 19 december than the normal distribution would suggest. If someone is interested in this kind of analysis, I could post the screenshots in this thread from time to time (for the beginning ES only). Cheers.

What do you expect to earn if you are correct and what do you expect to lose if you are wrong? That's the "equalizer".

nazzdack, it is a very good question I reply honestly: no idea. Maybe someone incorporates this information in his trading decisions, would it be very interesting to know how it can be used for practical trading.

I use this sorta thing occasionally (not for the S&P). There are all sorts of caveats to consider, however... If you want to look at an example of how this is done with a bit more rigor than just simply recovering the PDF from option prices, you could try here: http://www.clevelandfed.org/Research/Workpaper/2005/WP0507.pdf Obv, this is applied to FedFunds futures options, but the general methodology is sound.

Martinghoul, thank you for the answer! I know the paper you have referred to, the methodology of OLS is OK for Fed rates, because the meeting date is known in advance (basically, the date when the rate is changing is known), whereas in equity/FX the change can happen any time, so that's why I think this methodology cannot be applied that easily to equity/FX. And the other point is that the distribution might not have a shape of the normal distribution (e.g. look at the USDJPY 1Y distribution attached to this post, blue line is real distribution, pink is the atm log normal), then OLS will not yield a real risk-neutral distribution but just a normal which more or less fits the real one. Do you use PDF's for directional trading decisions or for volatility assessing or for something else? I am trying to implement options risk management based on PDF's, anyone interested in collaborating on this?

True points, I was just suggesting the FF paper as a general example of how much rigor is required to do the exercise properly. Simply relying on the estimated risk-neutral PDF is a strategy fraught with all sorts of peril. I occasionally use this type of analysis to get a sense of the distribution implied by option prices. If it's too out of whack with my expectations, it could help me identify interesting options trades.