yeah I have to admit I'm a little lost... I still don't know how to get to the implied distribution is there a book out there that gets into this stuff? Would Hull's book be the one? I'd really like to understand how I can calculate the implied distr from market IV's
Why don't you look at the patent document that was linked in one of the earlier posts? It contains a brief version of the explanation. I believe you can look in Hull for the full one.
Erol do you know how to get the implied distribution curve for one given IV? If not I am willing to explain in detail, I learned a lot since you started the topic In what language do you want to implement btw?
hey dennis, thanks for the offer! I want to take you up on it, b/c I don't yet... but I haven't had a chance to go through the patent doc yet. I don't think it would be fair to ask before I go through and read it. What do you mean by language? Programming language?
Yes I mean programming language, I presumed you did some programming yourself. I write my charts in java but I think it is very doable in excel also. There is a function for it I believe. I think you are better of trying to understand the implied distribution for one given IV first before you go any further, hence trying to understand that patent doc. I am not sure btw if it is usefull anyway to shoehorn all those IVs in one meaningfull curve but that should not spoil the fun finding out how to do it. I presume you understand a normal distribution curve, there is a 68% chance that a random value falls between 1 and -1 when mean=0 and stdev=1 etc. An underlying asset trading at 100 with an IV of 20% implies a 68% chance that it will trade between 80 and 120 a year from now. Hence the IV represents a 1 stdev price change in percentage for one year and the current underlying value as mean. Now it is easy to calculate the chance that the underlying trades at 70 one year from now, 70 represents -1,5 stdev=13% chanche, I will not go into details regarding the normal distribution (ND) function, excel has the function or software libraries are available for free. Because the BS option model is based on the distribution of price changes in percentages rather than absolute values one last step has to be taken to get the right curve. The input of the ND function doesn't change, you just have to give it another projection on the underlying value axis, normally that would be the x axis. Lets take 70 again, the chance was 13% so that will be the value for the y-axis. Basically you have to make a kind of continuously compounding interest calculation with IV as interest and mean as startpoint. The formula is <p>e<sup> (IV/100) * stdev </sup></p>, for our example the outcome is <p>e<sup> 0.2*-1.5 </sup></p> = 0.74 -> 100*0.74 = 74. Slightly more as 70 normally distributed. If you want a daily curve you divide the IV by sqrt 252, weekly by sqrt 52 etc. I wrapped it all up in an excel sheet
thank you so much Denis, I really appreciate you taking the time to explain it to me. I am aware of the ND function and all of that math. I've read and believe I understood Natenberg's book. So I must be missing something to converting the skews into a distribution... I suppose if I get all this stuff it's just a matter of me sitting down and making the connection. I'm sure I'm missing something trivial and I'll be like "ah-ha!". thanks again
This is not correct. ln(1.2) is not equal to -ln(0.8). If the asset is today at $100 and the natural logarithm of the price change is either 0.2 or -0.2, then the future price will be either $122.14 or $81.87. exp(0.2)=1,221402748 exp(-0.2)=0,818730753
yeah I was afraid I was going to say things you already knew, nevermind. I think I am just going to use a weighted average of IV between strikes.
your right, you can see that exact outcome in the sheet I attached, the 3th column is indeed useless. I took the example from Natenberg and now you point it out I dont understand why he says so in his book.