Variable step random walks, self-similar distributions, and pricing of options

Gemunu H. Gunaratne; Joseph L. McCauley

doi:10.1117/12.618948

23 May 2005 Variable step random walks, self-similar distributions, and pricing of options (Invited Paper)

Gemunu H. Gunaratne, Joseph L. McCauley

Proceedings Volume 5848, Noise and Fluctuations in Econophysics and Finance; (2005) https://doi.org/10.1117/12.618948
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

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.

Citation Download Citation

Gemunu H. Gunaratne and Joseph L. McCauley "Variable step random walks, self-similar distributions, and pricing of options (Invited Paper)", Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); https://doi.org/10.1117/12.618948

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