Testing the local volatility assumption: a statistical approach

In practice, the choice of using a local volatility model or a stochastic volatility model is made according to their respective ability to fit implied volatility surfaces. In this paper, we adopt an opposite point of view. Indeed, based on historical data, we design a statistical procedure aiming at testing the assumption of a local volatility model for the price dynamics, against the alternative of a stochastic volatility model.Local Volatility Models, Stochastic Volatility Models, Test Statistics, Semi-Martingales, Limit Theorems.