[richrichie]

Very few of the fancy models are actually used. Dupire's non parametric model has been the industrial work horse for a long time. Heston like SV's and Jump diffusions promised a lot and did not work in practice (calibration, stability issues). Some form of local stochastic models get used for certain products. In general, it is safe to say that Black-Scholes and its deterministic extension local vol have held up well.

[FabHK]

Not only that, but Dupire’s local vol, stochastic vol (Heston in rates, or on the equity side models that combine local vol with a stoch vol component to calibrate to implied vols perfectly) and jump diffusion were basically in production 15 years ago.

Since the GFC it’s not about crazy new products (on derivatives desks), but it’s about getting discounting/funding rates precisely right (depending on counterparty, collateral and netting agreements, onshore/offshore, etc), and about compliance and reporting.