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

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Abstract
We show that our earlier generalization of the BlackScholes partial differential equation (pde) for variable diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, the equivalence of BlackScholes 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 
Original Title:  Martingale option pricing 
Language:  English 
Keywords:  Markov process; option pricing; BlackScholes; Martingales; fat tails 
Subjects:  G  Financial Economics > G0  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C60  General 
Item ID:  2151 
Depositing User:  Joseph L. McCauley 
Date Deposited:  09. Mar 2007 
Last Modified:  07. Jan 2014 18:18 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/2151 