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)

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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.

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