Expanded smiles

Implied volatility smiles exist in all markets and have a significant effect on all option pricing and hedging. However, two models that produce the same initial prices for European-style options will not necessarily produce the same prices for exotics such as barrier options. Experience from the foreign exchange market suggests that barrier options are priced somewhere between the prices produced by pure local volatility models, à la Dupire (1994), and pure stochastic volatility models such as

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