We derive the local volatility hedge ratios that are consistent with a stochastic instantaneous volatility and show that this ‘stochastic local volatility’ model is equivalent to the market model for implied volatilities. We also show that a common feature of all Markovian single factor...

This paper extends the normal mixture diffusion (NMD) local volatility model of Brigo and Mercurio (2000, 2001a,b, 2002) so that it explains both short-term and long-term smile effects. Short-term smile effects are captured by a local volatility model where excess kurtosis in the price density...