  A homogeneously saturated equation for the time development of the price of a
financial asset is presented and investigated for the pricing of European call
options using noise that is distributed as a Student's t-distribution. In the
limit that the saturation parameter of the equation equals zero, the standard
model of geometric motion for the price of an asset is obtained. The
homogeneously saturated equation for the price of an asset is similar to a
simple equation for the output of a homogeneously broadened laser. The
homogeneously saturated equation tends to limit the range of returns and thus
seems to be realistic.
  Fits to linear returns obtained from the adjusted closing values for the S&P
500 index were used to obtain best-fit parameters for Student's t-distributions
and for normal distributions, and these fits were used to price options, and to
compare approaches to modelling prices.
  This work has value in understanding the pricing of assets and of European
call options.
