I should start by saying that I am not a quant, I am someone interested in options but I perhaps lack the mathematics background to always follow along. I recently stumbled upon a terrific article about trying to adjust for skew and basically trying to find which options were cheap/expensive on a skew adjusted basis: http://www.emanuelderman.com/media/strike_adjusted_spread.pdf

However, this where I got lost:

Instead, we will estimate the current risk-neutral return distribution Q( ) for a stock from its historical distribution P( ) by assuming that the latter is a plausible estimate for the former, and then requiring that the relative entropy S(P,Q) between the distributions is minimized.

How does one do this? I tried reading in the appendix and had a bit of a hard time following and I'm hoping one of you guys could perhaps explain?

Let's say I have a very simple stock with the following distribution:

$110: 25% of the time

$100: 50% of the time

$90: 25% of the time

And that is the entirety of the stock's possible distribution of prices.

How would I go about coercing this "historical" probability distribution into a risk-neutral probability distribution? If the exact math is too complicated perhaps a truncated/intuitive guesstimation? That would work for me as well.

If alternatively someone could provide me with a place where i could go to learn/read more (a paper where they did a step by step example would be best I suppose).

I appreciate any and all help.


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