I imagine they must use a modified Black-Scholes model with stochastic or implied volatility? And what do they do about the long tails of assets returns? Do they actually use the normal distribution? Thanks

It depends...

it depends if the tails go from -infinity to +infinity or not.

I talked to a prof. His impression is that people don't use Heston model a lot and Hull-White method can be more popular. This is contrary to academia. In finance research, Heston or Heston-Nandi is the only acceptable way. For jumps, I heard Credit Suisse has considered jump, but don't know whether it is only at explorative stage or not. Morgan Stanley HK is said to use SABR.

QuoteOriginally posted by: CulverinI talked to a prof. His impression is that people don't use Heston model a lot and Hull-White method can be more popular. This is contrary to academia. In finance research, Heston or Heston-Nandi is the only acceptable way. For jumps, I heard Credit Suisse has considered jump, but don't know whether it is only at explorative stage or not. Morgan Stanley HK is said to use SABR.Thanks

From my experience: yes and no.When it comes to plain vanilla options, then usually yes for pricing purposes. Banks usually have a system that constantly fits some parametric form or model to the Black-Scholes implied volatility smiles for the different maturities. When it then comes to quoting plain vanilla options, they just have to interpolate the resulting surface and use Black-Scholes to get the price. Nothing is lost this way since the volatility surface for any maturity incorporates all deviations from normality that are relevant for European payoffs. They might even do their real-time delta hedges based on the Black-Scholes delta, recompute the greeks under a more realistic model less frequently and keep track of the difference.For exotic options it is a clear no. I don't think anybody uses still Black-Scholes to price options with strong path dependence (e.g. barrier). However, when there is a need to the real-time market making of these products, then you need a closed-form solution and one common approach is again to price less frequently under a more realistic model, compute the deviation to some simple model with a closed-form solution (such as Black-Scholes) and then quote the options based on the price from the simple model plus a shift (i.e. the same thing that you do for the delta of vanillas).