Alpha-root Processes for Derivatives pricing

A class of mean reverting positive stochastic processes driven by alpha-stable distributions are discussed. A subclass of affine processes, they are referred to here as alpha-root processes in analogy to the square root process or the Cox-Ingersoll-Ross process derived from the Brownian motion. Being affine, they provide semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Their use has not been appreciated in the field perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a formulation that admits an efficient simulation algorithm to enable an extensive investigation of their properties.