Martingale option pricing

We show that our earlier generalization of the Black–Scholes partial differential equation (pde) for variable diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, the equivalence of Black–Scholes to a Martingale was proven for the case of the Gaussian returns model by Harrison and Kreps, but we prove it for a much larger class of returns models where the returns diffusion coefficient depends irreducibly on both returns xx and time tt. That option prices blow up if fat tails in logarithmic returns xx are included in market return is also proven.