Pricing exotics under the smile
The volatility implied from the market prices of vanilla options,using the Black-Scholes (1973) formula, varies withboth maturity and strike price. The typical, distinctiveshape of this volatility surface is generally referred to asthe volatility smile. The smile reflects departures of themarket from the assumptions underlying the Black-Scholesmodel. We refer to these violations of the Black-Scholes assumptionsas second-order effects.
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