McCauley, Joseph L. Gunaratne, Gemunu H. Bassler, Kevin E.
Abstract
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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
2151.
Find related papers by JEL classification: G0 - Financial Economics - - General C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
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