Regularization and analytic option pricing under -stable distribution of arbitrary asymmetry

Abstract

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an -stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the L\'evy propagator. Using distributional and C^n tools, we derive an analytic closed formula for the option price, valid for any stability ]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.

Tasks

Reproductions