NoNoNoAnd even if you did believe, why take expectations?No comment on cheap ways of raising smiles P

scholar, big, big differences. E.g. long and short positions have same value in your model (except for sign of course), and you get same value for a contract regardless of what it is hedged with. These not generally tue in uncertain vol models, which are highly nonlinear >>Paul, I understand this difference. But I was asking a different question: What in principle is bad with the idea that we have only a probabilistic knowledge of the true value of volatility, and therefore in the final answerr should integrate over all possible values of volatility with a probability density p(sigma) as the weight function ? What I said is that this idea can probably (again probably ) be considered more or less in line with what Fisher Black was talking about ?

I understand the maths of this Black model. What i question is the finance bit: do you think that it is possible that 1. vol is gonna be constant during the life of the option.2. it's gonna be either vol1 or vol2.3. vol1 with proba p, vol2 with proba 1-p.Or is it just a cheap way of getting a smile? >>Any question about a model that starts "do you think that it is possible. . ." can be answered "no." Models are impossible, that's why they're models. If they were possible, we'd call them reality.Black's mixture solution is, as you say, a cheap way of getting a smile. "Cheap" in the sense of minimizing parameters. BS uses constant volatility. If that doesn't give accurate enough results, try the simplest probability distribution before you go to GARCH.A lot of questions can be answered by writing down your best guesses of parameter values and computing. When that's not enough, you can try assuming simple probability distributions and see if that works. If not, you go to more complicated probability distributions and add parameters. But I find you rarely have to get to that third stage. People who spend a lot of time there do so because they like it.

Why didn't Black go the one extra, tiny, step and calculate standard deviations as well? And use that in the 'pricing.'P

if vol changes, shouldn't we be hedging vega to avoid losing money on volga (from the nonlinear relation between price and vol)?

I think he meant "really teaching". Which means...?

I think he meant "really teaching". Which means...? >>Which means the obvious. You can teach them from a mass produced textbook, show them how to jump through hoops, and make them think that they have learnt something. Why should that sort of teaching lead to good research?You can also tell them what things really mean, where things really come from, where the subject is currently heading, and basically help them rediscover it. That definitely leads to good research, because you have to understand the subject inside out before you can really teach it.

Omar,Hate to say it, but I think you are reading too much into Black's quote. I would take the quote at face value: since teaching is the only concrete service that a professor supplies, that's what he should be paid for.That's not to say that I agree with Black's comment; certainly good research creates an atmosphere where it is easier for a student to become interested in and learn new things. In my view, this is more valuable than the stuff you can pick up in a lecture room, but these sorts of things are hard to measure from a purely pragmatic viewpoint.Cheers,Hari

I understand the "really teaching" part, but not how Black could suggest that staff were paid on that basis; how does one quantify real teaching?Any qualitative measure could be aid to be subjective, and therefore irrelevant. Hari, doesn't research add value to the institution, by enhancing its reputation and therefore attracting more money?