On a New Parametrization Class of Solvable Diffusion Models and Transition Probability Kernels

We present in this paper a novel parametrization class of analytically tractable local volatility diffusion models used to price and hedge financial derivatives. A complete theoretical framework for computing the local volatility and the transition probability density is provided along with efficient model calibration for vanilla option prices, and reliable extrapolation procedures for producing the volatility surface. Our approach is based on the spectral analysis of the pricing operator in the time invariant case, along with some specific properties of the class that we propose. In order to show the advantages of our model, numerical examples with market data are analyzed. Finally, some extensions of our parametrization class are discussed in the conclusions