Martingale option pricing
J.L. McCauley,
G.H. Gunaratne and
K.E. Bassler
Physica A: Statistical Mechanics and its Applications, 2007, vol. 380, issue C, 351-356
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 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.
Keywords: Markov process; Option pricing; Black–Scholes; Kolmogorov backward equation; Martingales; Fat tails (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (18)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:380:y:2007:i:c:p:351-356
DOI: 10.1016/j.physa.2007.02.038
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