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

Gemunu H. Gunaratne·Joseph L. McCauley
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Abstract

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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Gemunu H. Gunaratne, Joseph L. McCauley. 2002-09-19. A theory for Fluctuations in Stock Prices and Valuation of their Options. https://arxiv.org/abs/cond-mat/0209475

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