  We consider a non-Gaussian option pricing model, into which the underlying
log-price is assumed to be driven by an $\alpha$-stable distribution. We remove
the a priori divergence of the model by introducing a Mellin regularization for
the L\'evy propagator. Using distributional and $\mathbb{C}^n$ tools, we derive
an analytic closed formula for the option price, valid for any stability
$\alpha\in]1,2]$ and any asymmetry. This formula is very efficient and recovers
previous cases (Black-Scholes, Carr-Wu); we calibrate the formula on market
datas, make numerical tests, and discuss its many interesting properties.
