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Stock 1) IV 25%, index weighting 20%
Stock 2) IV 20%, index weighting 30%
Stock 3) IV 20%, index weighting 25%
Stock 4) IV 15%, index weighting 20%
Stock 5) IV 35%, index weighting 5%

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

Stock 1) IV 25%, index weighting 20%
Stock 2) IV 20%, index weighting 30%
Stock 3) IV 20%, index weighting 25%
Stock 4) IV 15%, index weighting 20%
Stock 5) IV 35%, index weighting 5%

In this theoretical index, where all options are ATM, how would you calculate the fair value for the composite index ATM options ?
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17.3
 
Quote from Profitaker:

May I ask how you arrived at that figure ?
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from your sample the weighted basket IV=20.75 , then divide by 1.2 that represent ratio between the Index and amount of components (in this case , 5). The 1.2 is my own algorithm , so its all IMO.
Good luck
 
Quote from Profitaker:

I would have thought there would be correlation irrespective of direction, no ?
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Well, of course there is some correlation at all times. However, think about it intuitively - on the big bad days, every stock is down, even the best-of-the-best. The easiest way to convince yourself is to look at historical intraday correlatons vs the direction of the index on that day. More "quanty" way to think about it is to look at the implied index correlation at different deltas- that is to compare the weighted constituent vols at a given delta to index vol. You will see that implied correlation has a distinct put-side smirk to it.
 
Quote from Profitaker:

Thanks.

Wouldn't correlation need to be considered too ?
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of course it would. Assuming flat correlation, it would be

Basket Variance = Sum Vol(i)^2 * W(i)^2 +
Sum Sum Correlation / W(i) Vol(i) W(j) Vol(j)
 
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
 
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