Implied Distribution from Skew

Quote from henderson:

I would be interested in seeing your matlab code for the dirty implementation
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When did I ever say it was "dirty"?

Anyways, it's not exactly rocket science right here:
pp = spline(strikes, prices);
ppd = diffPP(pp);
ppdd = diffPP(ppd);

splitIncr = strikeStep / 2;
splitStrikes = [strikes(1)-splitIncr:splitIncr:strikes(end)+splitIncr]';
splitPrices = ppval(ppdd, splitStrikes);

for j = 1:length(strikes)-1
RNProbs(j) = trapz(splitStrikes(j*2-1:j*2+1),splitPrices(j*2-1:j*2+1));
end

This should work, if I haven't screwed anything up. Now I hope I don't go to jail for violating that crazy patent.
 
Quote from MasterAtWork:

It's useless to say that it needs to be rescaled to get the sum of probabilities equal to unity.

Masteratwork
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Certainly, "needless to say", but definitely not "useless to say", MAW.

You're absolutely correct, of course. I left out a few steps required to massage the results (such as discarding the insignificant points, normalizing, etc), as I thought they should be relatively self-explanatory.
 
Quote from Martinghoul:

Certainly, "needless to say", but definitely not "useless to say", MAW.

You're absolutely correct, of course. I left out a few steps required to massage the results (such as discarding the insignificant points, normalizing, etc), as I thought they should be relatively self-explanatory.
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ha ha ha, my bad, you're right :) .

Masteratwork
 
Sorry mixed up the wording; I wanted to make sure I was on the same page....I can usually see what someone is talking about much better by just seeing what they are trying to do in code!
 
Kevin,

Another name was "market gamma" some years ago.

Quote from Kevin Schmit:

I could swear that we used to call this technique "butterfly quadrature," but to my surprise I can't find a single Google hit on the term.
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Quote from dennisb:

In what sense differs the implied distribution from the implied deviation wich is the inverse log of IV/√days?
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I still dont understand the difference guys, I understood that the distribution curve is always the same but according to the suggestions I guess it is not. I understand the implied deviation but not the implied distribution, can somebody please explain, thx.
 
Quote from dennisb:

I still dont understand the difference guys, I understood that the distribution curve is always the same but according to the suggestions I guess it is not. I understand the implied deviation but not the implied distribution, can somebody please explain, thx.
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Implied risk neutral distribution is the risk neutral distribution extracted from market option prices. This risk neutral probability distribution, that is not the real one which can't be known, is just a tool to simplify pricing stuff for exotic options for example.

If there are different implied volties, that means that log returns are not normally distributed, and risk neutral distribution would exhibit skew and kurtosis.

Because options are traded on a market, implied volties move hence there're implied expected deviation and implied risk neutral distribution variations.

Masteratwork
 
Quote from MasterAtWork:

Implied risk neutral distribution is the risk neutral distribution extracted from market option prices. This risk neutral probability distribution, that is not the real one which can't be known, is just a tool to simplify pricing stuff for exotic options for example.

If there are different implied volties, that means that log returns are not normally distributed, and risk neutral distribution would exhibit skew and kurtosis.

Because options are traded on a market, implied volties move hence there're implied expected deviation and implied risk neutral distribution variations.

Masteratwork
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I managed to draw the annualized lognormal distribution curve of one strike with underlying at 351 with 0.20 IV, see attachment


but I am still not shure how to get something like this

http://www.elitetrader.com/vb/attachment.php?s=&postid=2668308 wich I assume represents the full chain and is what we are talking about, how would exp(-rT)(C1-2C2+C3)/d² lead to such? Could you give an example maybe to clear it up a bit.
 

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