McCauley, Joseph L. and Gunaratne, Gemunu H. (2003): An empirical model of volatility of returns and option pricing. Published in: Physica A , Vol. 329, (2003): pp. 178198.

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Abstract
This paper reports several entirely new results on financial market dynamics and option pricing We observe that empirical distributions of returns are much better approximated by an exponential distribution than by a Gaussian. This exponential distribution of asset prices can be used to develop a new pricing model for options (in closed algebraic form) that is shown to provide valuations that agree very well with those used by traders. We show how the FokkerPlanck formulation of fluctuations can be used with a local volatility (diffusion coeffficient) to generate an exponential distribution for asset returns, and also how fat tails for extreme returns are generated dynamically by a simple generalization of our new volatility model. Nonuniqueness in deducing dynamics from empirical data is discussed and is shown to have no practical effect over time scales much less than one hundred years. We derive an option pricing pde and explain why it‘s superfluous, because all information required to price options in agreement with the deltahedge is already included in the Green function of the FokkerPlanck equation for a special choice of parameters. Finally, we also show how to calculate put and call prices for a stretched exponential returns density.
Item Type:  MPRA Paper 

Institution:  University of Houston 
Original Title:  An empirical model of volatility of returns and option pricing 
Language:  English 
Keywords:  Market instability; market dynamics; finance; option pricing 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables G  Financial Economics > G0  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General 
Item ID:  2161 
Depositing User:  Joseph L. McCauley 
Date Deposited:  09. Mar 2007 
Last Modified:  12. Feb 2013 05:02 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/2161 