Food for thought: vega

I'm currently taking an options and futures class and my professor brought up a point about vega that I would like to share.

So, vega is defined as the rate of change of the value of the portfolio with respect to the volatility, sigma. But in the Black-Scholes model, sigma or volatility is assumed to be constant and known (which we all know is not true, volatility smiles and the like). So trying to measure the sensitivity of our portfolio (or option) to volatility while using a model that assumes volatility is constant, doesn't that seem kind of whack!

Just food for thought, I would love to hear how this is done in practice and anyone with some real-world experience can talk about it.
-fabz

 

Convexity of vol to a change in vol is expressed as dvega/dvol... important to understand when selling index options. Vega is occasionally referred to as "Kappa"

dvega/dspot is often more relevant in empirical runs and actual trading. Buy Paul Wilmott's book for a discussion of each.

 

Hi riskarb.

Which of his books discusses what you posted earlier in this thread? I looked at Amazon and he has a couple such as Wilmotts on financial derivatives or Wilmott introduces....,etc

Thanks

 

He might as well say the same thing about the whole BS model, not just vega...BS relies on a Gaussian assumption which Mandelbrot and others have long nailed as wrong and dangerous. So your Prof's comments are a blinding glimpse of the obvious.

On the other hand, BS is just a model and as such can be a useful tool, especially if you understand when not to use it.

 

Why only index options?

 

I think B&S assumes the volatility is constant with respect to time -- so you're using the same volatility till maturity. This does not mean your option value will not change if you change the volatility.

 

Not only, but vol-convexity is larger in index/equity

 

Damn, don't remember... I will take a look and PM you tonight.

 

Never knew that. I guess this is one of the challenges of arbitraging index vol against the vols of the underlying stocks.

From the perspective of the retail investor selling index options to generate cash and limit risk, the vol-convexity could be traded off for the benefits of diversifying away firm-specific risk.

 

What I don't get is how they justify ignoring the underlying asset drift. The lognormal assumption is bad enough but you can kind of rationalize it as a "needed" simplification. But if the asset drift is also ignored, how is that not insanely unrealistic?