We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic...

We propose a general class of non-constant volatility models with dependence on the past. The framework includes path-dependent volatility models such as that by Hobson&Rogers and also path dependent contracts such as options of Asian style. A key feature of the model is that market completeness...

We propose the use of a classical tool in PDE theory, the parametrix method, to build approximate solutions to generic parabolic models for pricing and hedging contingent claims. We obtain an expansion for the price of an option using as starting point the classical Black and Scholes formula....