QWARK


Total Posts: 23 
Joined: Apr 2008 


Hi,
If I am long USD 100k vega of option A ( implied vol of 10) and short USD 100k vega of option B ( implied vol of 100), which would be a better portfolio risk measure  the net vega of 0 or the net volatility weighted vega of 9000k (100k*10100k*100)? Someone told me that the latter risk measure incorporates "volofvol" which i did not understand fully.
Any thoughts?
Also, would be grateful if someone can kindly direct me to any academic paper that discuss the volatility weighted vega as a portfolio risk measure.
Thanks !
Q.




Baltazar


Total Posts: 1770 
Joined: Jul 2004 


It obviously depends on how option A and B are related. Same underlying, maturity, strike?
I believe you need to now how implied volatility of optioon A behaves compared to implied volatility of option B. One can do that through covariance of both volatilities or equivalently a function of correlation of both implied and vol of each vol.
This is just the same as : should I add the deltas of option A and B or not?

Qui fait le malin tombe dans le ravin 

aaron


Total Posts: 746 
Joined: Mar 2006 


Weighting by volatility is correct if the implied volatility of the options will change by the same multiplicative factor (if A goes from 10 to 11, B goes from 100 to 110). You wouldn't want to weight if the IV's would change by the same additive factor (if A goes from 10 to 11, B goes from 100 to 101).
As Baltazar says, the natural assumption depends on what kind of options you are comparing. If they have the same underlying and expiry, but B is a deep out of the money put, or if they have the same underlying and strike, but B has 100 times longer to expiry, or if they are totally unrelated (an S&P500 call versus a put on an individual stock); multiplicative makes more sense than additive. Of course, there is a lot of basis risk in those trades, you would be wise to consider gross as well as net Vega.
It's also possible to approach this with a model, like a vol surface or stochastic vol model. Then the model will dictate the total Vega. 



QWARK


Total Posts: 23 
Joined: Apr 2008 


Thanks Baltazar and Aaron for replying ! 


QWARK


Total Posts: 23 
Joined: Apr 2008 

 
niki5


Total Posts: 69 
Joined: Feb 2009 

 

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