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 volatility in extreme strike regimes, is widely recognised as an important risk management issue, first