  We show how effective-potential path-integrals methods, stemming on a simple
and nice idea originally due to Feynman and successfully employed in Physics
for a variety of quantum thermodynamics applications, can be used to develop an
accurate and easy-to-compute semi-analytical approximation of transition
probabilities and Arrow-Debreu densities for arbitrary diffusions. We
illustrate the accuracy of the method by presenting results for the
Black-Karasinski and the GARCH linear models, for which the proposed
approximation provides remarkably accurate results, even in regimes of high
volatility, and for multi-year time horizons. The accuracy and the
computational efficiency of the proposed approximation makes it a viable
alternative to fully numerical schemes for a variety of derivatives pricing
applications.
