An arbitrage-free interpolation of volatilities
Nabil Kahalé describes a new construction of an implied volatilities surface from a discrete set of implied volatilities that is arbitrage-free and satisfies some smoothness conditions. His method provides an excellent fit to the smile of the local volatilities model, a standard extension of the Black-Scholes model known to be hard to calibrate in practice. This allows the pricing of exotic options in a way consistent with the smile.
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