Stochastic Volatility Models

Every stochastic volatility model assumes yes stochastic volatility. All the stochastic volatility models I have looked into however assume constant volatility of volatility. Empirical research (mostly unpublished) shows the volatility of volatility is highly stochastic (make sure you not get tricked by sampling errors). Okay so what? Every model needs to make some assumptions. Models are only models. The problem is every stochastic volatility model I have looked at is highly sensitive to changes in the volatility of volatility. This combined with stochastic volatility of volatility is a rather bad combination. You do not know what the value of the option should be, and you do not know what the delta hedge should be. In particular out-of-the money options are extremely sensitive to the volatility of volatility (both the price and the hedge).

Stochastic volatility models are in general non-robust. They have moved the problem from one parameter to another parameter. And in addition they have added even more parameters to estimate (vol of vol, correlation between vol and underlying, bla bla bla.)

Well yes stochastic volatility models are better than the Black, Scholes and Merton model. But then knowledgeable traders do no use the Black, Scholes, Merton model. Yes they use the wording “Black-Scholes” or “Black-Scholes-Merton” but this do not mean that this is what they actually use. Trading is not about giving proper references to who did what when. GOOD Trading is about trying to make money, or at least making sure you not can blow up, traders use wording only for communication, few of them are too interested in getting their names in academic journals or about who published what. They don't even care if they call something A that actually not is A but B.

Quants and academics working with options think they have understood fat-tails for a very long time, because they have stochastic volatility models, jump-diffusion models, kurotsis adjusted models, local vol models etc etc.

Stochastic vol models and jump-diffusion models was however a nice attempt to move in the right direction, but I am afraid the approach "failed" compared to what many of us (including me) had hoped for.

So is the solution to extend stochastic volatility models to stochastic volatility of volatility models with constant volatility of volatility of volatility or to combine stochastic volatility with jumps and stochastic volatility surfaces. NO PLEASE STOP IT!. Yes you will probably get published something like that in a prestigious academic journal, but this is not giving us any improvements in practical option trading and hedging (the real problem to solve I personally think is in a completely different direction).

You will do far better than any of these models simply by using robust hedging principles like hedging options with options to truncate your exposure. But yes if your alternative is the naïve Black-Scholes-Merton approach of thinking you can hedge out almost all risk all the time by delta hedging yes then you should keep digging into stochastic volatility models and jump diffusion models.

But there is much more to this, and I will tell you much more later (probably).