Non-constant volatility models a comparison

Option pricing model with non-constant volatility models are compared to stochastic volatility ones. The non-constant volatility models considered are the Dupire's local volatility and Hobson and Rogers path-dependent volatility models. These approaches have the theoretical advantage of preserving the completeness of the market. The stochastic volatility models discussed are the Heston stochastic volatility and the SABR models. Because of their two-factor nature these models are notably flexible. The performances of the models are compared by considering their fit to the term structure of implied volatility, their robustness on the hedging and pricing of vanilla and exotic options.