Hello Everyone, I was looking for a good way to frame this question, but I could not come up with anything other than this. Are some volatility more expensive than other volatility?I understand that the volatility is a function of the model that we are using (like IV in the BS model), but is there any "model independent" answer to this, if there is such a thing at all.Not sure if the question makes a lot of sense. TIA.

Saying that "volatility is cheap/expensive" implicitly states that you are comparing risk-neutral / implied volatilities with the volatility of the underlying, data generating process (?).If so, then what you are referring to would be the 'volatility premium'... But I have the feeling that this is not the topic you are heading for, am I right?

There is the obvious observation that vega is highest for options with at-the-money-forward strikes, but that too is perhaps not what you are looking for. You might try checking out the stochastic dominance literature as applied to option pricing, that is a model independent approach if memory serves me correct.

QuoteOriginally posted by: Nimbus3000Hello Everyone, I was looking for a good way to frame this question, but I could not come up with anything other than this. Are some volatility more expensive than other volatility?I understand that the volatility is a function of the model that we are using (like IV in the BS model), but is there any "model independent" answer to this, if there is such a thing at all.Not sure if the question makes a lot of sense. TIA.Do you mean realized volatility of one stock vs realized volatility of other stock?

Let me try to explain my train of thought. Suppose there are two stocks. The historical volatility (say over 5 year) of one of them is say 20% and other is 40%. Now, some event takes place due to which the volatility of both of these stocks rise to 60%. If I am not looking at any model per se, should the premium for similar options on these stocks be the same as the volatility of both of them is the same or should the premium differ as the volatility of one of them has risen far more than that of the other. Again, I'm not sure if this makes a lot of sense but I've not been able to get my head around this.

Thanks DavidJN, I would look into it.

QuoteOriginally posted by: Nimbus3000Let me try to explain my train of thought. Suppose there are two stocks. The historical volatility (say over 5 year) of one of them is say 20% and other is 40%. Now, some event takes place due to which the volatility of both of these stocks rise to 60%. If I am not looking at any model per se, should the premium for similar options on these stocks be the same as the volatility of both of them is the same or should the premium differ as the volatility of one of them has risen far more than that of the other. Again, I'm not sure if this makes a lot of sense but I've not been able to get my head around this.Yes, the option premiums as measured by the implied volatility could well differ. The important idea is that the implied volatility of an option is a forward-looking quantity, as opposed to the historical volatility. Generally, the market anticipates that volatility will undergo mean-reversion, and so your 20% stock (with current vol. at 60%)may well have a lower premium than your 40% stock (with current vol. at 60%). But, it can work in the opposite direction too: maybe that 20% stock has an upcoming earnings releaseand the other stock doesn't. Then, the former may well have a higher premium.