A little confused, I consulted the Wilmott forums for guidance on how I can interpret vega/vomma. Another user's post reminded me that the Black-Scholes model assumes that the underlying has constant volatility, so vega is an out-of-model concept. If Black-Scholes assumes that volatility does not change, then would this not render vega/vomma calculations useless since they are based from the Black-Scholes formula? The vega calculation seems odd because one gauges how the option value changes with volatility, but then Black-Scholes assumes volatility does not change. Going a step further, the idea of vomma in a Black-Scholes world seems odd because if volatility does not change, then surely vega would not change?

I understand that Black-Scholes makes some questionable assumptions, but if we price options in a Black-Scholes world, then it seems peculiar that these metrics have come about as a result of the Black-Scholes formula. I would really appreciate any insight.

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    $\begingroup$ They are still useful as a measure of model risk. All models are wrong, some are useful. $\endgroup$ – experquisite Feb 4 '16 at 18:04

On the topic of your second paragraph, the author below is the authority on precisely that topic. Start at page 19



You are onto something, it is inconsistent to be calculating vega with Black-Scholes considering it assumes that volatility is constant.

Black-Scholes is not a good for modeling option prices/implied volatility. It's a very good intuitive model (like the CAPM), and a good way of organizing thoughts, but it is not an accurate depiction of reality. If it were, you wouldn't be seeing volatility smiles (it would be a noisy horizontal line instead).

If you're looking into modeling implied volatility, you should look into model free implied volatility which is based on risk neutral densities.


This is about implied volatility. Modeling realized volatility is another story.


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