Martingale option pricing

Joseph L. McCauley, Gemunu H. Gunaratne and Kevin E. Bassler

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Markov process; option pricing; Black-Scholes; Martingales; fat tails (search for similar items in EconPapers)
JEL-codes: C60 G0 (search for similar items in EconPapers)
Date: 2007-01-08
References: View complete reference list from CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/2151/1/MPRA_paper_2151.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:2151

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().