-factor local volatility function models for stock indices under a benchmark approach. It is assumed that the dynamics for a large …, the Dupire formula for the underlying local volatility function is recovered without assuming the existence of an … minimal market model are discussed as specific examples together with a smoothed local volatility function model that fits a …

For particular forms of a general volatility function, analytical solutions of the Black-Scholes PDE can be found …. However, it tends to be the case that the more 'realistic' the volatility function is, for instance with a volatility smile … the coefficients of the approximation. We show that for some particular forms of the volatility function those …