  The principle of absence of arbitrage opportunities allows obtaining the
distribution of stock price fluctuations by maximizing its information entropy.
This leads to a physical description of the underlying dynamics as a random
walk characterized by a stochastic diffusion coefficient and constrained to a
given value of the expected volatility, taking in this way into account the
information provided by the existence of an option market. This model is
validated by a comprehensive comparison with observed distributions of both
price return and diffusion coefficient. Expected volatility is the only
parameter in the model and can be obtained by analysing option prices. We give
an analytic formulation of the probability density function for price returns
which can be used to extract expected volatility from stock option data. This
distribution is of high practical interest since it should be preferred to a
Gaussian when dealing with the problem of pricing derivative financial
contracts.
