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.
|Item Type:||MPRA Paper|
|Institution:||University of Houston|
|Original Title:||Martingale option pricing|
|Keywords:||Markov process; option pricing; Black-Scholes; 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
|Depositing User:||Joseph L. McCauley|
|Date Deposited:||09. Mar 2007|
|Last Modified:||19. Feb 2013 01:26|
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