More sophisticated volatility models can better capture smiles, skew and stochastic volatility, but they also introduce new parameters and sources of uncertainty. Jumps, calibration and imperfect hedging show why greater model complexity does not necessarily mean lower risk.
Even with an advanced model, model risk persists Heston is a better conception: volatility varies, mean-reverts and rises when markets fall, generating the skew. It reduces misconception risk without removing it (no jumps, constant parameters) and, with five unobservable parameters instead of one, adds parameter (input) risk, in price and hedge (ranges below are illustrative). One quoted parameter against five inferred ones. σ is quoted as an implied volatility while Heston’s param