IVolatility Egar Service

[IV_Trader]

Quote from Profitaker:

Stock 1) IV 25%, index weighting 20% Correlation 0.90
Stock 2) IV 20%, index weighting 30% Correlation 1.10
Stock 3) IV 20%, index weighting 25% Correlation 1.25
Stock 4) IV 15%, index weighting 20% Correlation 0.72
Stock 5) IV 35%, index weighting 5% Correlation 1.10

In this theoretical index above, where all options are ATM, how would you calculate the fair value for the composite index ATM options ?

Any chance of a worked example if one you gets a chance ? TIA

probably pros can give better answer here , but I'l try...I don't think that single stock vs. index correl is important here (and maybe even very misleading) , its a basket's vs. index is what the most important. If the single stock over/under performing index , that will be reflected in his index weighting(back to the basket again). All IMO here.

 

[Profitaker]

Quote from IV_Trader:

probably pros can give better answer here , but I'l try...I don't think that single stock vs. index correl is important here (and maybe even very misleading) , its a basket's vs. index is what the most important.

I agree. But in my endeavour to learn, I need to start from basics. I need some help in the basic calc....Hence the above post.

I'm sure someone can help, he says...

 

[mysticman]

I have posted what Egar calls the following the main formula for dispersion. Taking the square root of both sides gives the volatility. Notice that correlation is in the formula, and I believe this to be the correlation of the IV of the components.

The Egar goes on to say: "There are several ways to calculate the risk of the index. Theoretical Index Volatility can be calculated from the formula of portfolio dispersion, or as a weighted sum of components’ volatilities (WtdCompIV %). The simplest method to calculate an index volatility is to consider it as a weighted sum of volatilities of its components. This sum will be called weighted components implied volatility, or weighted volatility of index. The weighted volatility of index calculated this way expresses overall implied volatility of the index components, but ignores correlation between component stocks...
The ratio of the components implied volatility (WtdCompIV %) to actual implied index volatility hereinafter will be referred to as a first volatility level coefficient." IV_Trader says that he uses the ratio of 1.2, but this is actually at the lower end of the range for this coefficient/ratio.

 

[Profitaker]

mystic

Thanks, I have the formula. Just need someone to work an example....

 

[sle]

Quote from mysticman:
I believe this to be the correlation of the IV of the components.

No, it is the correlation of the changes in the underlying. If you want to be really correct, you should use separate correlation for every pair, but it is not too hard to derive the same formula for the index to component correlation (the correlation of the two components to each other would be a weighted ratio of the two correlations to the index).

 

[IV_Trader]

went long Index - short components this month , left out crazy GM.
DIA premium on ATM straddle is so low , represents only 2% of the nominal , IMO it's almost insanity to short at those levels.
I think it's going to be a lot of "help!!!" posts on SPX credit journal thread...

 

[Profitaker]

Quote from IV_Trader:

went long Index - short components this month , left out crazy GM.

How do you choose the components ? What percentage weighting of the index do you replicate with your basket of stocks.

Thanks.

 

[mysticman]

I had some old monthly data I was working with recently and thought you'd like to see how the historical volatility of the index compares with the weighted sum of the volatilities of its components, which in this case are the Dow stocks so they are already price weighted. I used the HV of the OEX as a proxy for the Dow.

 

[Profitaker]

mystic

Very interesting, many thanks. A compelling case for a reverse dispersion trade then ?

 

[mysticman]

Quote from Profitaker:
Very interesting, many thanks. A compelling case for a reverse dispersion trade then ?

No. It depends on the relationship of IV to SV. IV on the index can still be expensive.