  The standard Black-Scholes theory of option pricing is extended to cope with
underlying return fluctuations described by general probability distributions.
A Langevin process and its related Fokker-Planck equation are devised to model
the market stochastic dynamics, allowing us to write and formally solve the
generalized Black-Scholes equation implied by dynamical hedging. A systematic
expansion around a non-perturbative starting point is then implemented,
recovering the Matacz's conjectured option pricing expression. We perform an
application of our formalism to the real stock market and find clear evidence
that while past financial time series can be used to evaluate option prices
before the expiry date with reasonable accuracy, the stochastic character of
volatility is an essential ingredient that should necessarily be taken into
account in analytical option price modeling.
