Munich Personal RePEc Archive

Martingale option pricing

McCauley, Joseph L. and Gunaratne, Gemunu H. and Bassler, Kevin E. (2007): Martingale option pricing. Forthcoming in: Physica A (2007)


Download (602kB) | Preview


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 much a much larger class of returns models where the returns diffusion coefficient depends irreducibly on both returns x and time t. That option prices blow up if fat tails in logarithmic returns x are included in market return is also proven.

MPRA is a RePEc service hosted by
the Munich University Library in Germany.