Vega or volatility weighted Vega - Which is a better portfolio risk measure ?

QWARK · Post by **QWARK** » Fri Mar 20, 2009 9:08 pm

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*10-100k*100)? Someone told me that the latter risk measure incorporates "vol-of-vol" 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 · Post by **Baltazar** » Sun Mar 22, 2009 7:14 pm

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?

aaron · Post by **aaron** » Mon Mar 23, 2009 3:00 am

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 · Post by **QWARK** » Thu Mar 26, 2009 11:26 pm

Thanks [url=/User/Show%20User%20Details.aspx?UserIDKey=142]Baltazar[/url] and Aaron for replying !

QWARK · Post by **QWARK** » Sun Mar 29, 2009 3:46 pm

Hi

Attached is a presentation by Jim Gatheral where he has empirically observed that the implied variance is approximately log-normally distributed, i.e. dsigma proportional to sigma. This is very intuitive; vols should move around more if the volatility level is 100% than if it is 10%. Vol weighted vega attempts to do exactly this.

http://finmath.stanford.edu/seminars/docs/ml2004win.pdf

http://www.math.nyu.edu/fellows_fin_math/gatheral/barcelona2003.pdf

Thnx

Q.

niki5 · Post by **niki5** » Wed Apr 01, 2009 2:42 pm

Ho QWARK,

take a look here:

1993 "Opportunities and Perils of Using Option Sensitivities," The Journal of Financial Engineering

http://www.espenhaug.com/articles.html

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