  A master equation approach to the numerical solution of option pricing models
is developed. The basic idea of the approach is to consider the Black--Scholes
equation as the macroscopic equation of an underlying mesoscopic stochastic
option price variable. The dynamics of the latter is constructed and formulated
in terms of a master equation. The numerical efficiency of the approach is
demonstrated by means of stochastic simulation of the mesoscopic process for
both European and American options.
