A theory for Fluctuations in Stock Prices and Valuation of their Options

Details A theory for Fluctuations in Stock Prices and Valuation of their Options A theory for Fluctuations in Stock Prices and Valuation of their Options

2002-09-19

arxiv.org/abs/cond-mat/0209475v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends 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 provide an alternative mechanism to implement the new options pricing formulae derived from our theory.

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