Index constituent weightings and implied volatilities

basically yes , but on the paper only. And I can bring one example when even if all are at +1 , it will not stand : huge skew on Index's put that will heavily weighted on mean Index IV.

 

I'd be interested in that example.

 

my previous post WAS an example. Look back around mid June ( when market tanked and huge skew on OTM puts existed) and see how basket/index vols relationship changed drastically, while the correl stayed the same. Its shows you that one cannot simple use the components correl to calculate Index's IV .
Anyway , good to see you posting again , did you had any success trading dispersion lately ?

 

Don't follow that statement - the index IV is calculated using the BS model (or similar), likewise the components. The (implied) correlation between components and index is derived in the same way that one would calculate the volatility of any portfolio.

Edit: Actually the correlation (correl as you call it) didn't stay the same - component correlation increased as the market tanked, which is why the "basket/index vols relationship changed drastically".

Always reading IV_Trader, but posting only when I have something to contribute.

Trading reverse dispersion / long correlation, yes.

 

you can delete up to 1/2 hour after!

 

Thanks Electric.

I'm fine up until my 2nd bottle of wine.

Hic

 

Profitaker,

"Depends how stocks A & B were correlated"

Mathematically speaking, I am somewhat retarded. I'm guessing that "+1" means if X moves +1, Y moves +1 (and I stand corrected).

How do you derive the 19.12% figure?

How is the "implied index correlation (IIC)" determined (please use my examples)?

Re your FTSE IIC of 0.44, does this mean that for a 1% change in the IV of the constituents, the FTSE IV will change + 0.44%?

If this is a lack of 1:1 correlation, it may be due to the lack of options on some constituents and unwittingly, you may have saved me an awful lot of work – if no option is traded, then extrapolation becomes increasingly problematic(al?).

Another problem is contiguous data. Once an initial IV has been determined, higher/lower volatility is apparent from the premiums (or premia if you want to be pedantic). But to actually nail the IV's of the sum of the constituents and index at the point of execution may be a nightmare – unless it is blatant (then again, I've always thought, if you see an arbitrage opportunity, ignore it because it doesn't exist) .

Alternative potential candidates – I haven't checked – are DAX, CAC, SMI and DJ Euro Stoxx.

Do you use any software. I write my own, inspired by a product called Schwartzatron by Reuters. At the time (1990) they were charging £20,000 pa just to rent. And round the same time, an article in the Wall Stret Journal mentioned a product called Shark used by traders at Goldman Sachs.

Are you in the UK (where)? I'm in a sleepy fishing village called Manchester.

Rosy2,

Using my examples, obtain the eigenvalues and explain what they are/mean; also explain why they would provide a better insight than the weightings as stated. Show all workings, and please keep it simple.

IV Trader,

I'm just trying to establish the theoretical basis. It may never happen; not all the conditions of Black-Scholes are fully met but it is still used as a (plain vanilla) starting point.

I'm not looking to determine the index IV from the constituent's IV's – as you say, skew (smirk and smile) may throw that out of the window. Further, the constituents would exhibit skew, etc. Who wants to be a quant?

Grant.

 

Excuse me for butting in, but I work in this field for my personal trading and find these discussions few and far between.

I have found correlations to be ranges representing deviations measured numerically..

It does not need to be an exact science. Leave the exactness for the quants with programs arbing the "thing". It is up to us manual traders to discover the instruments that they have not.

Michael B.

 

i am referring to principal component analyis. eigen values/vectors can be obtained from a covarince/correlatin matrix of your basket constituent returns. they tell you which stocks in your basket move more/less with the whole.

 

going back to your original Q ; the more components in the Index the lesser is Index's IV ( vs weighed basket IV).
Ask P-taker how to calculate it , if I remember correctly , he got the formula from Sle way back.
Good luck