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In this work we present an analytical model, based on the path-integralformalism of Statistical Mechanics, for pricing options using first-passagetime problems involving both fixed and deterministically moving absorbingbarriers under possible non-gaussian distributions of the underlying object. Weadapt to our problem a model originally proposed to describe the formation ofgalaxies in the universe of De Simone et al (2011), which uses cumulantexpansions in terms of the Gaussian distribution, and we generalize it to takeinto acount drift and cumulants of orders higher than three. From theprobability density function, we obtain an analytical pricing model, not onlyfor vanilla options (thus removing the need of volatility smile inherent to theBlack-Scholes model), but also for fixed or deterministically moving barrieroptions. Market prices of vanilla options are used to calibrate the model, andbarrier option pricing arising from the model is compared to the price resultedfrom the relative entropy model.

Analytical Path-Integral Pricing of Moving-Barrier Options under non-Gaussian Distributions