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Proceedings Paper

Variable step random walks, self-similar distributions, and pricing of options
Author(s): Gemunu H. Gunaratne; Joseph L. McCauley
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Paper Abstract

A new theory for pricing of options is presented. It is based on the assumption that successive movements depend on the value of the return. The solution to the Fokker-Planck equation is shown to be an asymmetric exponential distribution, similar to those observed in intra-day currency markets. The "volatility smile", used by traders to correct the Black-Scholes pricing is shown to be a heuristic mechanism to implement options pricing formulae derived from our theory.

Paper Details

Date Published: 23 May 2005
PDF: 9 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.618948
Show Author Affiliations
Gemunu H. Gunaratne, Univ. of Houston (United States)
Joseph L. McCauley, Univ. of Houston (United States)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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