Rational shapes of local volatility

The asymptotic behaviour of local volatility surfaces for low and high strikes – the so-called wings – is important in option pricing and risk management. Stefano De Marco, Peter Friz and Stefan Gerhold show certain models allow for the derivation of analytic forms, using saddle-point methods

Robust implementation of a Dupire-type local volatility model (Dupire, 1994) is important for every equity option trading floor. Typically, this problem is solved in a two-step procedure: a smooth parameterisation of the implied volatility surface; and computation of the local volatility based on the resulting call prices. The first of these, and in particular how to extrapolate the implied