Martingale option pricing

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

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.

• Item Type: MPRA Paper
• Institution: University of Houston
• Language: English
• Keywords: Markov process; option pricing; Black-Scholes; Martingales; fat tails
• Subjects: G - Financial Economics > G0 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C60 - General

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