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

Author

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  • Gemunu H. Gunaratne
  • Joseph L. McCauley

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.

Suggested Citation

  • Gemunu H. Gunaratne & Joseph L. McCauley, 2002. "A theory for Fluctuations in Stock Prices and Valuation of their Options," Papers cond-mat/0209475, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0209475
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    Cited by:

    1. J.L. McCauley & G.h. Gunaratne, 2002. "An empirical model of volatility of returns and option pricing," Computing in Economics and Finance 2002 186, Society for Computational Economics.
    2. McCauley, Joseph L., 2003. "Thermodynamic analogies in economics and finance: instability of markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 199-212.
    3. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "An empirical model of volatility of returns and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 178-198.
    4. McCauley, Joseph L., 2004. "What Economists can learn from physics and finance," MPRA Paper 2240, University Library of Munich, Germany.
    5. McCauley, Joseph L., 2004. "Making dynamic modelling effective in economics," MPRA Paper 2130, University Library of Munich, Germany.
    6. McCauley, Joseph L., 2003. "Scaling, correlations, and cascades in finance and turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 213-221.
    7. McCauley, Joseph l., 2004. "Thermodynamic analogies in economics and finance: instability of markets," MPRA Paper 2159, University Library of Munich, Germany.

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